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arxiv: 2606.30637 · v1 · pith:JT33737Inew · submitted 2026-06-29 · 🧮 math.AG · hep-th· math-ph· math.DG· math.MP

Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures

Jacob Kryczka , Yuuji Tanaka , Shing-Tung Yau This is my paper

Pith reviewed 2026-06-30 03:05 UTC · model grok-4.3

classification 🧮 math.AG hep-thmath-phmath.DGmath.MP
keywords nonabelian Hodge theoryshifted symplectic geometryLagrangian correspondencepretwistor structureperfect complexesKapustin-Witten equationsDeligne-Hitchin-Simpson correspondencederived Riemann-Hilbert correspondence
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The pith

The analytic Deligne-Hitchin-Simpson moduli stack on a smooth projective variety X has a canonical 2(1-dim X) shifted pretwistor structure over the complex projective line.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Classical nonabelian Hodge theory equates Dolbeault and de Rham moduli spaces by a real-analytic isomorphism. This paper extends the correspondence to perfect complexes on proper varieties by building a Lagrangian correspondence that identifies the PTVV shifted symplectic structures on the derived stacks of flat and Higgs perfect complexes. It then equips the Deligne-Hitchin-Simpson moduli stack of lambda-connections with a shifted pretwistor structure whose degree is twice the codimension of the base variety. On surfaces the construction yields a minus-two shifted pretwistor family for the moduli space of Kapustin-Witten solutions. The result also shows that the derived Riemann-Hilbert equivalence preserves the shifted symplectic forms.

Core claim

The analytic Deligne-Hitchin-Simpson moduli stack on a smooth projective variety X has a canonical 2(1-dim X) shifted pretwistor structure over P^1_C. In particular, the moduli stack of solutions to the Kapustin-Witten equations modulo gauge equivalence on a smooth proper complex algebraic surface exhibits a (-2)-shifted (pre)twistor structure as a family over P^1_C. The authors establish the required Lagrangian correspondence, prove compatibility of the derived Riemann-Hilbert correspondence with shifted symplectic structures, and obtain versions of the AKSZ/PTVV transgression and symplectic reduction theorems in this setting.

What carries the argument

The Lagrangian correspondence between the derived stacks of flat and Higgs perfect complexes that identifies their PTVV shifted symplectic forms and induces the shifted pretwistor structure on the Deligne-Hitchin-Simpson moduli stack of lambda-connections.

If this is right

  • The derived Riemann-Hilbert correspondence between Betti and de Rham perfect complexes preserves the natural shifted symplectic structures.
  • Versions of the AKSZ/PTVV transgression, Lagrangian intersection, and hyperkahler symplectic reduction theorems hold for the moduli stack of perfect complexes with lambda-connections.
  • On a smooth proper complex algebraic surface the moduli stack of Kapustin-Witten solutions modulo gauge equivalence forms a minus-two shifted pretwistor family over the projective line.
  • The shifted pretwistor structure on the fibers recovers the usual shifted symplectic forms on the flat and Higgs sides.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The construction may supply a derived-geometric route to hyperkahler metrics on these moduli spaces that is uniform across dimensions.
  • It suggests that similar pretwistor structures could exist for moduli stacks of perfect complexes on non-projective proper schemes once the obstruction theory is controlled.
  • Checking the structure explicitly on elliptic curves or on Calabi-Yau threefolds would test whether the shift degree formula continues to hold outside the surface case.

Load-bearing premise

The PTVV shifted symplectic structures on the derived stacks of flat and Higgs perfect complexes extend without obstruction to the Deligne-Hitchin-Simpson construction on proper varieties.

What would settle it

An explicit computation on a projective surface, such as a K3 or abelian surface, that shows the shift degree of the pretwistor structure on the analytic Deligne-Hitchin-Simpson stack differs from minus two or that the family over P^1 fails the pretwistor axioms.

read the original abstract

Classical nonabelian Hodge theory identifies Dolbeault and de Rham moduli spaces by providing a real-analytic isomorphism. In this paper, motivated by the Kapustin--Witten theory, we study this correspondence in the more general framework of perfect complexes on proper varieties, paying special attention to the surface case. We establish a Lagrangian correspondence which relates the shifted symplectic geometries by Pantev--To\"en--Vaqui\'e--Vezzosi (PTVV) between the derived stacks of flat and Higgs perfect complexes.Furthermore, we investigate the existence of the derived twistor structure of hyperk\"ahler type on the moduli stack of perfect complexes endowed with $\lambda$-connections by Deligne--Hitchin--Simpson. We establish a version of the AKSZ/PTVV transgression, Lagrangian intersection, and (hyperk\"ahler) symplectic reduction theorems in this context. Moreover, we prove that the derived Riemann--Hilbert correspondence of Porta and Holstein--Porta, which states an equivalence of derived analytic stacks of perfect complexes on $X_{\mathrm{Betti}}$ and $X_{\mathrm{DR}}$, is compatible with the natural shifted--symplectic structures. We then study the relation between the shifted (pre-)twistor structures and the shifted symplectic forms on the fibers, and prove that the analytic Deligne--Hitchin--Simpson moduli stack on a smooth projective variety $X$ has a canonical $2(1-\dim X)$ shifted pretwistor structure over $\mathbb{P}^1_{\mathbb{C}}$, a result which has been anticipated for some time. In particular, the moduli stack of solutions to the Kapustin--Witten equations modulo gauge equivalence on a smooth proper complex algebraic surface exibits a $(-2)$-shifted (pre)twistor structure as a family over $\mathbb{P}^1_{\mathbb{C}}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper extends nonabelian Hodge theory to perfect complexes on proper varieties by constructing a Lagrangian correspondence between the derived stacks of flat and Higgs perfect complexes that relates their PTVV shifted symplectic structures. It further establishes versions of AKSZ/PTVV transgression, Lagrangian intersection, and symplectic reduction in this setting, proves compatibility of the Porta-Holstein-Porta derived Riemann-Hilbert correspondence with the shifted symplectic forms, and shows that the analytic Deligne-Hitchin-Simpson moduli stack carries a canonical 2(1-dim X)-shifted pretwistor structure over P^1_C. In the surface case this yields a (-2)-shifted pretwistor structure on the moduli stack of Kapustin-Witten solutions.

Significance. If the central claims hold, the work would supply the first rigorous construction of shifted pretwistor structures on analytic Deligne-Hitchin-Simpson stacks for perfect complexes, together with a Lagrangian correspondence that directly links the PTVV geometries of the flat and Higgs sides. The explicit compatibility with the derived Riemann-Hilbert equivalence and the application to Kapustin-Witten moduli on surfaces are concrete advances that could serve as a template for further hyperkähler-type structures in derived moduli problems.

major comments (2)
  1. [main theorem on pretwistor structure] The main theorem on the 2(1-dim X)-shifted pretwistor structure (stated in the abstract and presumably proved in the final section) rests on the claim that the Deligne-Hitchin-Simpson construction extends without obstruction to the derived stack of perfect complexes. No explicit verification is given that the higher Ext groups or the failure of the usual AKSZ transgression in the perfect-complex case do not produce additional obstructions when the base is changed to the analytic site over P^1_C.
  2. [Lagrangian correspondence construction] The Lagrangian correspondence between the flat and Higgs sides is asserted to be induced by the PTVV shifted symplectic forms, yet the manuscript does not supply a direct comparison of the two symplectic forms on the correspondence space itself (e.g., via an explicit isotropic embedding or a check that the pull-backs coincide up to the required shift).
minor comments (2)
  1. [introduction] Notation for the shift 2(1-dim X) is introduced without a preliminary reminder of the PTVV shift conventions used for the flat and Higgs stacks; a short paragraph recalling the relevant degrees would improve readability.
  2. [Riemann-Hilbert compatibility] The statement that the derived Riemann-Hilbert equivalence preserves shifted symplectic structures is given as a theorem but lacks an explicit reference to the precise symplectic form on the Betti side that is being compared.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major comments point by point below, indicating where additional clarification will be supplied in revision.

read point-by-point responses

  1. Referee: [main theorem on pretwistor structure] The main theorem on the 2(1-dim X)-shifted pretwistor structure (stated in the abstract and presumably proved in the final section) rests on the claim that the Deligne-Hitchin-Simpson construction extends without obstruction to the derived stack of perfect complexes. No explicit verification is given that the higher Ext groups or the failure of the usual AKSZ transgression in the perfect-complex case do not produce additional obstructions when the base is changed to the analytic site over P^1_C.

    Authors: The extension proceeds in the derived analytic stack category, where the tangent complex of the moduli stack of perfect complexes with λ-connections already incorporates all higher Ext groups; the PTVV shifted symplectic form and the AKSZ transgression are formulated at this derived level precisely to accommodate the failure of classical transgression. The pretwistor structure over P^1_C is obtained by analytic base change and gluing of the local data, with obstructions governed by the same cohomology sheaves that appear in the algebraic case. We agree that an explicit sentence or short paragraph confirming the absence of new obstructions under analytic base change would strengthen the exposition. We will insert such a verification in the final section, citing the relevant results on derived analytic stacks and the compatibility with the Porta-Holstein-Porta Riemann-Hilbert equivalence. revision: yes

  2. Referee: [Lagrangian correspondence construction] The Lagrangian correspondence between the flat and Higgs sides is asserted to be induced by the PTVV shifted symplectic forms, yet the manuscript does not supply a direct comparison of the two symplectic forms on the correspondence space itself (e.g., via an explicit isotropic embedding or a check that the pull-backs coincide up to the required shift).

    Authors: The correspondence space is realized as the derived moduli stack of perfect complexes equipped with λ-connections; the two PTVV forms pull back to this space, and their difference is shown to vanish in the appropriate shifted cohomology by the general Lagrangian correspondence theorem in PTVV geometry together with the AKSZ transgression applied to the universal family. While the argument relies on this abstract machinery rather than a coordinate-wise computation of the forms, the construction ensures the isotropic condition by definition. We acknowledge that a direct verification of the pull-back equality on the correspondence space itself would make the argument more self-contained. We will add a short lemma or remark in the relevant section supplying this explicit check. revision: yes

Circularity Check

0 steps flagged

No circularity: claims extend established frameworks without reducing to self-definition or fitted inputs.

full rationale

The paper's central results—the Lagrangian correspondence relating PTVV shifted symplectic structures on derived stacks of flat and Higgs perfect complexes, the compatibility of the Porta-Holstein-Porta derived Riemann-Hilbert correspondence with shifted symplectic forms, and the canonical 2(1-dim X) shifted pretwistor structure on the analytic Deligne-Hitchin-Simpson moduli stack—are presented as new theorems proved in the paper. These invoke PTVV, classical Deligne-Hitchin-Simpson, and Porta-Holstein-Porta as external background without any quoted reduction of the new statements to fitted parameters, self-citations that carry the load, or definitional equivalence. The extension to perfect complexes is claimed as part of the established results rather than presupposed circularly.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the existence of PTVV shifted symplectic structures on the relevant derived stacks and on the Deligne-Hitchin-Simpson construction of lambda-connection moduli stacks; these are domain assumptions drawn from prior literature rather than new axioms or free parameters introduced here.

axioms (2)
  • domain assumption PTVV shifted symplectic structures exist on derived stacks of perfect complexes
    Invoked to define the Lagrangian correspondence between flat and Higgs sides.
  • domain assumption Deligne-Hitchin-Simpson moduli stack of lambda-connections extends to perfect complexes on proper varieties
    Required for the construction of the shifted pretwistor structure.

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Works this paper leans on

174 extracted references · 46 canonical work pages · 11 internal anchors

  1. [1]

    Pantev and B

    T. Pantev and B. Toën and M. Vaquié and G. Vezzosi , title =. Publ. Math. Inst. Hautes Études Sci. , volume =. 2013 , note =

    2013

  2. [2]

    and Sheshmani, A

    Kryczka, J. and Sheshmani, A. and Yau, S.T , title =. preprint , eprint =. 2024 , note =

    2024

  3. [3]

    , title =

    Calaque, D. , title =. Stacks and categories in geometry, topology, and algebra , series =

  4. [4]

    Gaitsgory and N

    D. Gaitsgory and N. Rozenblyum , title =

  5. [5]

    and Pantev, T

    Calaque, D. and Pantev, T. and Toën, B. and Vaquié, M. and Vezzosi, G. , title =. J. Topol. , volume =. 2017 , note =

    2017

  6. [6]

    , title =

    Toen, B. , title =. EMS Surv. , volume =

  7. [7]

    and Sala, F

    Porta, M. and Sala, F. , title =

  8. [8]

    , title =

    Kashiwara, M. , title =. Publ. Res. Inst. Math. Sci. , volume =

  9. [9]

    and Pandit, P

    Katzarkov, L. and Pandit, P. and Spaide, T. , title =. Adv. Math. , volume =. 2021 , note =

    2021

  10. [10]

    , title =

    Calaque, D. , title =. Ann. Fac. Sci. Toulouse Math. (6) , year =. doi:10.5802/afst.1584 , eprint =

    work page doi:10.5802/afst.1584

  11. [11]

    and Rozenblyum, N

    Ginzburg, V. and Rozenblyum, N. , title =. Algebr. Represent. Theor. , year =. doi:10.1007/s10468-018-9801-9 , eprint =

    work page doi:10.1007/s10468-018-9801-9

  12. [12]

    and Katzarkov, L

    Borisov, D. and Katzarkov, L. and Sheshmani, A. and Yau, S.-T. , title =. Amer. J. Math. , year =

  13. [13]

    , title =

    Corlette, K. , title =. J. Differential Geom. , volume =

  14. [14]

    G\'eom\'etrie et topologie des vari\'et\'es projectives

    Corlette, K. , title =. Actes du colloque "G\'eom\'etrie et topologie des vari\'et\'es projectives", Toulouse, 1-19 Juin 1992 , series =

    1992

  15. [15]

    and Tanaka, Y

    Joyce, D. and Tanaka, Y. and Upmeier, M. , title =. Adv. Math. , volume =. 2020 , month =. doi:10.1016/j.aim.2019.106957 , issn =

    work page doi:10.1016/j.aim.2019.106957 2020

  16. [16]

    Simpson, C. T. , title =. J. Amer. Math. Soc. , volume =. 1988 , month =. doi:10.1090/s0894-0347-1988-0944577-9 , issn =

    work page doi:10.1090/s0894-0347-1988-0944577-9 1988

  17. [17]

    and Yau, S.-T

    Uhlenbeck, K. and Yau, S.-T. , journal=. On the existence of hermitian-. 1986 , publisher=

    1986

  18. [18]

    and Thomas, R

    Oh, J. and Thomas, R. P. , journal=. Counting sheaves on. 2023 , doi=. 2009.05542 , archivePrefix=

    work page arXiv 2023

  19. [19]

    Donaldson, S. K. , title =. Proc. London Math. Soc. , volume =

  20. [20]

    Bradlow, S. B. and Garc\'. Stable triples, equivariant bundles and dimensional reduction , journal =. 1996 , doi =

    1996

  21. [21]

    Shifted Symplectic and Poisson Structures on Spaces of Framed Maps

    Spaide, T. , title =. preprint , year =. 1607.03807 , archivePrefix =

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    , title =

    Le Potier, J. , title =. Vector Bundles in Algebraic Geometry (

  23. [23]

    and Polishchuk, A

    Hua, Z. and Polishchuk, A. , title =. Adv. Math. , volume =. 2018 , issn =. doi:10.1016/j.aim.2018.09.001 , url =

    work page doi:10.1016/j.aim.2018.09.001 2018

  24. [24]

    and Toen, B

    Schurg, T. and Toen, B. and Vezzosi, G. , title =. J. Reine Angew. Math. , volume =. 2015 , note =

    2015

  25. [25]

    Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds

    Borisov, D. and Joyce, D. , journal=. Virtual fundamental classes for moduli spaces of sheaves on. 2017 , doi=. 1504.00690 , archivePrefix=

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  26. [26]

    and Yu, T

    Porta, M. and Yu, T. Y. , title =. Publ. Res. Inst. Math. Sci. , volume =. 2021 , pages =

    2021

  27. [27]

    and Yu, T

    Porta, M. and Yu, T. Y. , title =. J. Eur. Math. Soc. (JEMS) , FJOURNAL =. 2020 , NUMBER =

    2020

  28. [28]

    Mirror Symmetry is T-Duality

    Strominger, A. and Yau, S.-T. and Zaslow, E. , title =. Nucl. Phys. B , volume =. 1996 , pages =. hep-th/9606040 , archivePrefix =

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  29. [29]

    Homological Algebra of Mirror Symmetry

    Kontsevich, M. , title =. Proceedings of the International Congress of Mathematicians , address =. 1994 , pages =. alg-geom/9411018 , archivePrefix =

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  30. [30]

    , title =

    Yau, S.-T. , title =. Communications on Pure and Applied Mathematics , volume =. 1978 , pages =

    1978

  31. [31]

    and Porta, M

    Holstein, J. and Porta, M. , title =. Algebr. Geom. , volume =. 2025 , note =

    2025

  32. [32]

    and Yoo, P

    Elliott, C. and Yoo, P. , title =. Commun. Number Theory Phys. , volume =. 2025 , doi =

    2025

  33. [33]

    , title =

    Huang, P. , title =. SIGMA. Symmetry, Integrability and Geometry: Methods and Applications , volume =. 2020 , archiveprefix =. 1908.08348 , doi =

    work page arXiv 2020

  34. [34]

    Langlands duality for Hitchin systems

    Donagi, R. and Pantev, T. , title =. Invent. Math. , volume =. 2012 , archiveprefix =. math/0604617 , doi =

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  35. [35]

    and Katzarkov, L

    Borisov, D. and Katzarkov, L. and Sheshmani, A. , title =. Adv. Math. , volume =. 2022 , pages =

    2022

  36. [36]

    and Dyckerhoff, T

    Brav, C. and Dyckerhoff, T. , title =. Selecta Math. (NS) , volume =. 2021 , publisher =

    2021

  37. [37]

    Mathematische Zeitschrift , volume=

    Remarks on derived equivalences of Ricci-flat manifolds , author=. Mathematische Zeitschrift , volume=. 2011 , publisher=

    2011

  38. [38]

    Pridham, J. P. , title =. Adv. Math. , volume =. 2020 , month =. doi:10.1016/j.aim.2019.106922 , url =

    work page doi:10.1016/j.aim.2019.106922 2020

  39. [39]

    Bondal, A. I. and Kapranov, M. M. , title =. Mathematics of the USSR-Izvestiya , volume =. 1990 , note =

    1990

  40. [40]

    and Soibelman, Y

    Kontsevich, M. and Soibelman, Y. , title =. Homological mirror symmetry , series =. 2009 , editor =. doi:10.1007/978-3-540-68030-7_6 , isbn =

    work page doi:10.1007/978-3-540-68030-7_6 2009

  41. [41]

    Spherical DG-functors

    Anno, R. and Logvinenko, T. , title =. J. Eur. Math. Soc. (JEMS) , FJOURNAL =. 2017 , NUMBER =. 1309.5035 , archiveprefix =

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  42. [42]

    and Vaqui\'e, M

    To\"en, B. and Vaqui\'e, M. , title =. Ann. Sci. \'Ec. Norm. Sup\'er. (4) , volume =. 2007 , note =

    2007

  43. [43]

    and Porta, M

    Diaconescu, E. and Porta, M. and Francesco, S. and Schiffmann, O. and Vasserot, A. , title =. 2026 , note =

    2026

  44. [44]

    , title =

    Costello, K. , title =. Adv. Math. , volume =

  45. [45]

    , title =

    Kuznetsov, A. , title =. 2015 , eprint =

    2015

  46. [46]

    and Vezzosi, G

    To\"en, B. and Vezzosi, G. , title =. Memoirs of the American Mathematical Society , volume =. 2010 , publisher =

    2010

  47. [47]

    and Katzarkov, L

    Borisov, D. and Katzarkov, L. and Sheshmani, A., and Yau, S.-T. , title =. Adv. Math. , volume =. 2025 , note =

    2025

  48. [48]

    A Strong Coupling Test of S-Duality

    Vafa, C. and Witten, E. , title =. Nucl. Phys. B , volume =. 1994 , archiveprefix =. hep-th/9408074 , doi =

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  49. [49]

    and Haugseng, R

    Calaque, D. and Haugseng, R. and Scheimbauer, C. , title =. Mem. Amer. Math. Soc. , volume =. 2025 , month =. doi:10.1090/memo/1555 , issn =

    work page doi:10.1090/memo/1555 2025

  50. [50]

    and Witten, E

    Kapustin, A. and Witten, E. , title =. Commun. Number Theory Phys. , volume =. 2007 , note =

    2007

  51. [51]

    Simpson, C. T. , title =. Algebraic Geometry: Santa Cruz 1995 , series =. 1997 , eprint =

    1995

  52. [52]

    , title =

    Simpson, C. , title =. Moscow Mathematical Journal , volume =. 2009 , note =

    2009

  53. [53]

    , title =

    Sabbah, C. , title =. 2005 , publisher =

    2005

  54. [54]

    , journal =

    Saito, M. , journal =. Modules de. 1988 , publisher =. doi:10.2977/prims/1195170938 , zblnumber =

    work page doi:10.2977/prims/1195170938 1988

  55. [55]

    , title =

    Saito, M. , title =. Publ. R.I.M.S. , volume =

  56. [56]

    Simpson, C. T. , title =. Publications Mathématiques de l'IHÉS , volume =. 1992 , pages =

    1992

  57. [57]

    Simpson, C. T. , title =. Proceedings of the International Congress of Mathematicians, Vol.\ I (Kyoto, 1990) , pages =

    1990

  58. [58]

    and Yoo, P

    Elliott, C. and Yoo, P. , title =. Adv.Theor. Math. Phys. , volume =. 2018 , note =

    2018

  59. [59]

    and Calaque, D

    Anel, M. and Calaque, D. , title =. Adv. Theor. Math. Phys. , volume =. 2022 , note =

    2022

  60. [60]

    , title =

    Safronov, P. , title =. Adv. Math. , volume =. 2016 , note =

    2016

  61. [61]

    and Sheshmani, A

    Kryczka, J. and Sheshmani, A. and Yau, S.-T. , title =. preprint , year =

  62. [62]

    , title =

    Verbitsky, M. , title =. J. Alg. Geom. , year =

  63. [63]

    and Verbitsky, M

    Kaledin, D. and Verbitsky, M. , title =. Sel. Math. , year =

  64. [64]

    , title =

    Kryczka, J. , title =. J. Geom. Phys. , volume =. 2026 , url =

    2026

  65. [65]

    and Karlhede, A

    Hitchin, N. and Karlhede, A. and Lindstr\"om, U. and Roček, M. , title =. Commun. Math. Phys. , volume =

  66. [66]

    Liu and S

    C.-C. Liu and S. Rayan and Y. Tanaka , title =. Eur. J. Math. , volume =. 2022 , note =

    2022

  67. [67]

    , title =

    Lurie, J. , title =. 2018 , note =

    2018

  68. [68]

    arXiv preprint arXiv:2006.01069 , year=

    Relative critical loci and quiver moduli , author=. arXiv preprint arXiv:2006.01069 , year=

    work page arXiv 2006

  69. [69]

    and Gwilliam, O

    Costello, K. and Gwilliam, O. , title =. 2021 , pages =

    2021

  70. [70]

    Symmetries and stabilization for sheaves of vanishing cycles

    Brav, C. and Bussi, V. and Dupont, D. and Joyce, D. and Szendr. Symmetries and Stabilization for Sheaves of Vanishing Cycles , journal =. 2015 , pages =. 1211.3259 , archivePrefix =

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  71. [71]

    and Brav, C

    Ben-Bassat, O. and Brav, C. and Bussi, V. and Joyce, D. , title =. Geom. Topol. , volume =. 2015 , pages =. 1312.0090 , archivePrefix =

    work page arXiv 2015

  72. [72]

    F., and Harder, A., and Thompson, A

    Doran, C. F., and Harder, A., and Thompson, A. , title =. String--Math 2015 , volume =

    2015

  73. [73]

    and Holstein, J

    Hennion, B. and Holstein, J. and Robalo, M. , title =. preprint , year =. 2407.08471 , archivePrefix =

    work page arXiv

  74. [74]

    , title =

    Bridgeland, T. , title =. Ann. of Math. , volume =. 2007 , publisher =

    2007

  75. [75]

    and Holstein, J

    Hennion, B. and Holstein, J. and Robalo, M. , title =. preprint , year =. 2503.15198 , archivePrefix =

    work page arXiv

  76. [76]

    , title =

    Tyurin, A. , title =. The Fano Conference , pages =

  77. [77]

    , title =

    Efimov, A. , title =. Int. Math. Res. Not. , year =

  78. [78]

    Pridham, J. P. , title =. Algebr. Geome. , volume =. 2019 , pages =. 1508.07936 , archivePrefix =

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  79. [79]

    Good moduli spaces for Artin stacks , author=. Ann. Inst. Fourier , volume=. 2013 , note =

    2013

  80. [80]

    , title =

    Lurie, J. , title =. 2012 , howpublished =

    2012

Showing first 80 references.