相关论文: Framed motivic Donaldson-Thomas invariants of smal…
We compute the motivic Donaldson-Thomas theory of small crepant resolutions of toric Calabi-Yau 3-folds.
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 prove a motivic version of the Donaldson--Thomas/Pandharipande--Thomas (DT/PT) correspondence on Calabi--Yau threefolds. The proof combines Toda's wall crossing framework and the motivic integral identity recently proved by Bu. This…
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 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 prove the motivic version of the DT/PT-correspondence in \cite{PT} and the motivic flop formula of the curve counting invariants in the derived category of smooth Calabi-Yau threefold DM stacks. The main method we use is Bridgeland's…
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…
We compute the motivic Donaldson-Thomas theory of the resolved conifold, in all chambers of the space of stability conditions of the corresponding quiver. The answer is a product formula whose terms depend on the position of the stability…
We study motivic Donaldson-Thomas invariants in the sense of Behrend-Bryan-Szendroi. A wall-crossing formula under a mutation is proved for a certain class of quivers with potentials.
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 define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category ("number of BPS states with given charge" in…
We compute, via motivic wall-crossing, the generating function of virtual motives of the Quot scheme of points on $\mathbb{A}^3$, generalising to higher rank a result of Behrend, Bryan and Szendr\H{o}i. We show that this motivic partition…
For a Calabi-Yau 3-fold $X$, we explicitly compute the Donaldson-Thomas type invariant counting pairs $(F, V)$, where $F$ is a zero-dimensional coherent sheaf on $X$ and $V\subset F$ is a two dimensional linear subspace, which satisfy a…
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…
Given a quiver with potential associated to a toric Calabi-Yau threefold, the numerical Donaldson-Thomas invariants for the moduli space of framed representations can be computed by using toric localization, which reduces the problem to the…
We provide a reduction formula for the motivic Donaldson-Thomas invariants associated to a quiver with superpotential. The method is valid provided the superpotential has a linear factor, it allows us to compute virtual motives in terms of…
We prove the crepant resolution conjecture for Donaldson-Thomas invariants of toric Calabi-Yau 3-orbifolds with transverse A-singularities.
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 $\mathbb{C}^4/G$,…
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…
In recent years, a version of enumerative geometry over arbitrary fields has been developed and studied by Kass-Wickelgren, Levine, and others, in which the counts obtained are not integers but quadratic forms. Aiming to understand the…