相关论文: Counting invariants for the ADE McKay quivers

We propose a conjecture that relates some local Gromov-Witten invariants of some crepant resolutions of Calabi-Yau 3-folds with isolated singularities with some Donaldson-Thomas type invariants of the moduli spaces of representations of…

We present a local computation of deformations of the tangent bundle for a resolved orbifold singularity C^d/G. These correspond to (0,2)-deformations of (2,2)-theories. A McKay-like correspondence is found predicting the dimension of the…

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…

We compute the Donaldson-Thomas invariants for two types of Calabi-Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are…

We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence we establish a wall-crossing formula for the…

We establish a geometric interpretation of orientifold Donaldson-Thomas invariants of $\sigma$-symmetric quivers with involution. More precisely, we prove that the cohomological orientifold Donaldson-Thomas invariant is isomorphic to the…

Let $G\subset SL_2(C)\subset SL_3(C)$ be a finite group. We compute motivic Pandharipande-Thomas and Donaldson-Thomas invariants of the crepant resolution $Hilb^G(C^3)$ of $C^3/G$ generalizing results of Gholampour and Jiang who computed…

We prove a comparison formula for curve-counting invariants in the setting of the McKay correspondence, related to the crepant resolution conjecture for Donaldson-Thomas invariants. The conjecture is concerned with comparing the invariants…

The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…

Let $X$ be a complex four-dimensional compact Calabi-Yau manifold equipped with a K\"ahler form $\omega$ and a holomorphic four-form $\Omega$. Under certain assumptions, we define Donaldson-Thomas type deformation invariants by studying the…

We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber)…

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical…

Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient $\mathbb{C}^4/G$,…

We construct curve counting invariants for a Calabi-Yau threefold $Y$ equipped with a dominant birational morphism $\pi:Y \to X$. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when…

We study the relationship between derived categories of factorizations on gauged Landau-Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions on the variation, we show the derived…

We study the BPS invariants of the preferred Calabi-Yau resolution of ADE polyhedral singularities C^3/G given by Nakamura's G-Hilbert schemes. Genus 0 BPS invariants are defined by means of the moduli space of torsion sheaves as proposed…

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…

Supersymmetric D-branes supported on the complex two-dimensional base $S$ of the local Calabi-Yau threefold $K_S$ are described by semi-stable coherent sheaves on $S$. Under suitable conditions, the BPS indices counting these objects (known…

We compute motivic Donaldson-Thomas invariants for crepant resolutions of quotients of affine three-space by even dihedral groups in terms of an affine type D root system, using double dimensional reduction and the representation theory of…

For a finite abelian group G in GL(n,k), we describe the coherent component Y_theta of the moduli space M_theta of theta-stable McKay quiver representations. This is a not-necessarily-normal toric variety that admits a projective birational…