相关论文: Donaldson-Thomas Theory and Resolutions of Toric T…
For any toric Calabi-Yau 3-orbifold with transverse A-singularities, we prove Ruan's crepant resolution conjecture and the Gromov-Witten/Donaldson-Thomas correspondence.
We compute the motivic Donaldson-Thomas theory of small crepant resolutions of toric Calabi-Yau 3-folds.
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 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 aim of this paper is to study an analog of non-commutative Donaldson-Thomas theory corresponding to the refined topological vertex for small crepant resolutions of toric Calabi-Yau 3-folds. We define the invariants using dimer models…
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…
We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz CY3 orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equality of rational functions. In order to do so, we show that…
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…
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…
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…
Let $X$ be a compact complex Calabi-Yau 4-fold. Under certain assumptions, we define Donaldson-Thomas type deformation invariants ($DT_{4}$ invariants) by studying moduli spaces of solutions to the Donaldson-Thomas equations on $X$. We also…
We prove an open version of Ruan's Crepant Transformation Conjecture for toric Calabi-Yau 3-orbifolds, which is an identification of disk invariants of K-equivalent semi-projective toric Calabi-Yau 3-orbifolds relative to corresponding…
We define Donaldson-Thomas invariants of Calabi-Yau orbifolds and we develop a topological vertex formalism for computing them. The basic combinatorial object is the orbifold vertex, a generating function for the number of 3D partitions…
The goal of the present paper is to show the transformation formula of Donaldson-Thomas invariants on smooth projective Calabi-Yau 3-folds under birational transformations via categorical method. We also generalize the non-commutative…
We modify the standard perfect symmetric obstruction theory for moduli spaces of simple perfect complexes, to the situation of complexes on abelian threefolds with fixed determinant and Fourier-Mukai determinant. As outcome we attach…
We present a construction of Donaldson-Thomas invariants for three-dimensional projective Calabi-Yau Deligne-Mumford stacks. We also study the structure of these invariants for etale gerbes over such stacks.
We study higher rank Donaldson-Thomas invariants of a Calabi-Yau 3-fold using Joyce-Song's wall-crossing formula. We construct quivers whose counting invariants coincide with the Donaldson-Thomas invariants. As a corollary, we prove the…
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…
This paper is motivated by the question of how motivic Donaldson--Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi--Yau threefolds, defined by quivers with homogeneous…
Given a complex 4-fold $X$ with an (Calabi-Yau 3-fold) anti-canonical divisor $Y$, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of $Y$. We also discuss gluing formulas…