相关论文: Motivic DT-invariants for the one loop quiver with…
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 derive some combinatorial consequences from the positivity of Donaldson-Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Efimov. These results are used to prove the Kac conjecture for…
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…
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 review several algebraic, combinatorial and geometric interpretations of motivic Donaldson-Thomas invariants of symmetric quivers.
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 for a class of quivers with potentials using the strategy of Behrend, Bryan, and Szendroi. This class includes quivers with potentials arising from consistent brane tilings and quivers with zero…
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.
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…
We show that motivic Donaldson-Thomas invariants of a~symmetric quiver $Q$, captured by the generating function $P_Q$, can be encoded in another quiver $Q^{(\infty)}$ of (almost always) infinite size, whose only arrows are loops, and whose…
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 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…
In this paper we calculate the motivic Donaldson-Thomas invariants for (-2)-curves arising from 3-fold flopping contractions in the minimal model programme. We translate this geometric situation into the machinery developed by Kontsevich…
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…
Levine has constructed motivic analogues of virtual fundamental classes, living in cohomology of Witt sheaves. We use this to define motivic Donaldson-Thomas invariants $\tilde{I}_n$ for $\mathbb{P}^3$ over $\mathbb{R}$. We show that for…
Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In…
Donaldson-Thomas invariant is expressed as the weighted Euler characteristic of the so-called Behrend (constructible) function. In \cite{Behrend} Behrend introduced a DT-type invariant for a morphism. Motivated by this invariant, we extend…
We study tilting for the heart A of the canonical t-structure of the finite-dimensional derived category of the Ginzburg algebra for a quiver with potential (Q,W). We give conditions on that the stable objects for a central charge on A…
We construct and study Donaldson-Thomas invariants counting orthogonal and symplectic objects in linear categories, which are a generalization of the usual Donaldson-Thomas invariants from the structure groups $\mathrm{GL} (n)$ to the…
We compute the motivic Donaldson-Thomas theory of small crepant resolutions of toric Calabi-Yau 3-folds.