For crepant resolutions X(1,3,9) and X(1,3,13) the derived categories admit faithful braid twist group actions of types D and E induced by spherical object configurations.
Calabi-Yau algebras
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution. In dimension 3, the resolution is determined by a noncommutative potential. Representation varieties of the Calabi-Yau algebra are intimately related to the set of critical points, and to the sheaf of vanishing cycles of the potential. Numerical invariants, like ranks of cyclic homology groups, are expected to be given by `matrix integrals' over representation varieties. We discuss examples of Calabi-Yau algebras involving quivers, 3-dimensional McKay correspondence, crepant resolutions, Sklyanin algebras, hyperbolic 3-manifolds and Chern-Simons. Examples related to quantum Del Pezzo surfaces will be discussed in [EtGi].
verdicts
UNVERDICTED 6representative citing papers
Establishes wall-crossing for Calabi-Yau four dg-quivers and local CY fourfolds via refined vertex algebras and a new stable infinity-categorical framework for virtual pullbacks.
Proves that for any d ≥ 1, twisted (d+2)-periodic algebras correspond to algebraic triangulated categories with a dZ-cluster tilting object that admit a unique dg enhancement.
Compact Fukaya categories of general plumbings are generated by proper modules over associated Ginzburg dg algebras and equivalent to proper modules over wrapped Fukaya categories and to microlocal sheaves.
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
Neural networks classify Seiberg dual classes on Z_m x Z_n orbifolds with R^2=0.988 and predict toric multiplicities for Y^{6,0} with mean absolute error 0.021 under fixed Kasteleyn representative.
citing papers explorer
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Some faithful algebraic braid twist group actions for 3-fold crepant resolutions
For crepant resolutions X(1,3,9) and X(1,3,13) the derived categories admit faithful braid twist group actions of types D and E induced by spherical object configurations.
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Wall-crossing for Calabi-Yau fourfolds: framework, tools, and applications
Establishes wall-crossing for Calabi-Yau four dg-quivers and local CY fourfolds via refined vertex algebras and a new stable infinity-categorical framework for virtual pullbacks.
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The Derived Auslander-Iyama Correspondence
Proves that for any d ≥ 1, twisted (d+2)-periodic algebras correspond to algebraic triangulated categories with a dZ-cluster tilting object that admit a unique dg enhancement.
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Proper modules over Ginzburg dg algebras and compact Fukaya categories of plumbings
Compact Fukaya categories of general plumbings are generated by proper modules over associated Ginzburg dg algebras and equivalent to proper modules over wrapped Fukaya categories and to microlocal sheaves.
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Quiver Yangians as Coulomb branch algebras
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
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Machine Learning Toric Duality in Brane Tilings
Neural networks classify Seiberg dual classes on Z_m x Z_n orbifolds with R^2=0.988 and predict toric multiplicities for Y^{6,0} with mean absolute error 0.021 under fixed Kasteleyn representative.