Topic
Crepant resolution
About: Crepant resolution is a research topic. Over the lifetime, 344 publications have been published within this topic receiving 7987 citations.
Papers published on a yearly basis
Papers
TL;DR: Gonzalez-Sprinberg and Verdier as discussed by the authors interpreted the McKay correspondence as an isomorphism on K theory, observing that the representation of G is equal to the G-equivariant K theory of C2.
Abstract: The classical McKay correspondence relates representations of a finite subgroup
G ⊂ SL(2,C) to the cohomology of the well-known minimal resolution of the
Kleinian singularity C2/G. Gonzalez-Sprinberg and Verdier [10] interpreted the
McKay correspondence as an isomorphism on K theory, observing that the representation
ring of G is equal to the G-equivariant K theory of C2. More precisely,
they identify a basis of the K theory of the resolution consisting of the classes of
certain tautological sheaves associated to the irreducible representations of G.
769 citations
1 Jan 2004
TL;DR: In this article, the notion of non-commutative crepant resolution of a singularity was introduced and shown to exist in certain cases. And they also gave some evidence for an extension of a conjecture by Bondal and Orlov, stating that different resolutions of a Gorenstein singularity have the same derived category.
Abstract: We introduce the notion of a “non-commutative crepant” resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category.
402 citations
Posted Content•
TL;DR: In this paper, it was shown that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a crepant resolution of X=M/G and that there is a derived equivalence (Fourier- Mukai transform) between coherent sheaves on Y and coherent G-sheaves on M.
Abstract: Let G be a finite group of automorphisms of a nonsingular complex threefold M such that the canonical bundle omega_M is locally trivial as a G-sheaf. We prove that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a crepant resolution of X=M/G and that there is a derived equivalence (Fourier- Mukai transform) between coherent sheaves on Y and coherent G-sheaves on M. This identifies the K theory of Y with the equivariant K theory of M, and thus generalises the classical McKay correspondence. Some higher dimensional extensions are possible.
382 citations
TL;DR: In this article, it was shown that the orbifold Chow ring of the toric Deligne-Mumford stack associated to a simplicial toric variety is a flat deformation of (but not necessarily isomorphic to) the Chow ring.
Abstract: Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. The main result in this paper is an explicit calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an application, we prove that the orbifold Chow ring of the toric Deligne-Mumford stack associated to a simplicial toric variety is a flat deformation of (but is not necessarily isomorphic to) the Chow ring of a crepant resolution.
284 citations
TL;DR: In this article, the authors define a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson-Thomas invariants for Calabi-Yau threefolds.
Abstract: Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A–modules, analogous to rank–1 Donaldson–Thomas invariants of Calabi–Yau threefolds. For the special case when A is the non-commutative crepant resolution of the threefold ordinary double point, it is proved using torus localization that the invariants count certain pyramid-shaped partition-like configurations, or equivalently infinite dimer configurations in the square dimer model with a fixed boundary condition. The resulting partition function admits an infinite product expansion, which factorizes into the rank–1 Donaldson–Thomas partition functions of the commutative crepant resolution of the singularity and its flop. The different partition functions are speculatively interpreted as counting stable objects in the derived category of A–modules under different stability conditions; their relationship should then be an instance of wall crossing in the space of stability conditions on this triangulated category.
228 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 17 |
| 2020 | 17 |
| 2019 | 22 |
| 2018 | 20 |
| 2017 | 26 |