Related papers: Donaldson Thomas invariant of P^1 scroll

We relate the Donaldson invariants of two four-manifolds $X_i$ with embedded Riemann surfaces of genus 2 and self-intersection zero with the invariants of the manifold X which appears as a connected sum along the surfaces. When the original…

Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a nonsingular threefold X in three different situations: (1). X is a K3 fibration over a…

Let X be the total space of the canonical bundle of P^2. We study the generalized Donaldson-Thomas invariants, defined in the work of Joyce-Song, of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern…

This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks. In this paper, we present the construction of Donaldson-Thomas invariants for general…

Let $X$ and $X'$ be nonsingular projective $3$-folds related by a flop of a disjoint union of $(-2)$-curves. We prove a flop formula relating the Donaldson-Thomas invariants of $X$ to those of $X'$, which implies some simple relations among…

Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers DT^a(t) which count stable sheaves with Chern character a on X, with respect to a Gieseker stability condition t. They are defined only for Chern…

Let $X$ be a (-1)-shifted symplectic derived Deligne--Mumford stack. In this paper we introduce the Darboux stack of $X$, parametrizing local presentations of $X$ as a derived critical locus of a function $f$ on a smooth formal scheme $U$.…

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…

The main result of this paper is the statement that the Hodge theoretic Donaldson-Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure…

Generalized Donaldson-Thomas invariants defined by Joyce and Song arXiv:0810.5645 are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on a Calabi-Yau 3-fold $X$, where…

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…

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…

Generalized Donaldson-Thomas invariants corresponding to local D6-D2-D0 configurations are defined applying the formalism of Joyce and Song to ADHM sheaves on curves. A wallcrossing formula for invariants of D6-rank two is proven and shown…

This is a survey of the book arXiv:0810.5645 with Yinan Song. Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers DT^a(t) which count stable sheaves with Chern character a on X, with respect to a Gieseker…

Let $S$ be a projective simply connected complex surface and $\mathcal{L}$ be a line bundle on $S$. We study the moduli space of stable compactly supported 2-dimensional sheaves on the total spaces of $\mathcal{L}$. The moduli space admits…

We compute the zero-dimensional Donaldson-Thomas invariants of the quotient stack $[\mathbb{C}^4/\mathbb{Z}_r]$, confirming a conjecture of Cao-Kool-Monavari. Our main theorem is established through an orbifold analogue of Cao-Zhao-Zhou's…

We prove that Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli spaces. In particular, such invariants depend only on the scheme structure of the moduli space, not the symmetric obstruction theory…

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…

The wall-crossing formula for Donaldson invariants of smooth, simply connected four manifolds with $b^+=1$ is shown to be a topological invariant of the manifold for reducible connections with two or fewer singular points. The explicit…

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…