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.
Ginzburg, Calabi-- Y au algebras , arXiv:math/0612139 (2006)
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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].
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UNVERDICTED 3representative 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.
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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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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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.