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Quantum cohomology of blowups

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arxiv 2307.13555 v3 pith:BT7XBYPK submitted 2023-07-25 math.AG math.SG

Hiroshi Iritani This is my paper · ORCID
classification math.AGmath.SG
keywords cohomologyquantumsmoothalonganalysisblowupblowupsd-module
verification ladder T0 review T1 audit T2 compute T3 formal
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We prove a decomposition theorem of the quantum cohomology D-module of the blowup of a smooth projective variety X along a smooth subvariety Z. The main tools we use are shift operators and Fourier analysis for equivariant quantum cohomology.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum spectrum and Gamma structure for standard flips

    math.AG 2025-02 conditional novelty 7.0 of 10

    For standard flips, the extremal quantum spectrum is shown to be compatible with the Gamma-class decomposition and with the semi-orthogonal decompositions of Orlov and Belmans-Fu-Raedschelders.

  2. The cubic threefold is symplectically irrational

    math.SG 2026-08 conditional novelty 6.0 of 10

    The cubic threefold is symplectically irrational, proved via the formal monodromy of its quantum connection.

  3. An atomic criterion for irrationality without quantum computations

    math.AG 2026-07 conditional novelty 6.0 of 10

    Under monodromy-irreducibility and vanishing-cohomology size bounds, Hodge-general Fano hyperplane sections of Fano fivefolds are irrational without explicit atom computations.

  4. Moduli of atoms of complex projective varieties

    math.AG 2026-07 conditional novelty 6.0 of 10

    For rank-r connections with pole order at most 2, nilpotent leading term, and non-resonant semisimple monodromy, every connected component of the coarse moduli space is the affine space n⊕n, of dimension r(r−1).

  5. The quantum D-module of product varieties

    math.AG 2025-09 reject novelty 6.0 of 10

    The quantum D-module of a product of smooth projective varieties is formally isomorphic to the tensor product of the factors' quantum D-modules, making atoms multiplicative and the atom map a ring homomorphism.

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