Related papers: Local contributions to Donaldson-Thomas invariants

Oberdieck and Pandharipande conjectured that the curve counting invariants of $S\times E$, the product of a $K3$ surface and an elliptic curve, is given by minus the reciprocal of the Igusa cusp form of weight 10. For a fixed primitive…

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…

We show that the Quot scheme $Q_L^n = \textrm{Quot}_{\mathbb A^3}(\mathscr I_L,n)$ parameterising length $n$ quotients of the ideal sheaf of a line in $\mathbb{A}^3$ is a global critical locus, and calculate the resulting motivic partition…

For $g,n\geq 0$ a 3-dimensional Calabi-Yau $A_\infty$-category $\mathcal C_{g,n}$ is constructed such that a component of the space of Bridgeland stability conditions, $\mathrm{Stab}(\mathcal C_{g,n})$, is a moduli space of quadratic…

We study Hilbert schemes of points on a smooth projective Calabi-Yau 4-fold $X$. We define $\mathrm{DT}_4$ invariants by integrating the Euler class of a tautological vector bundle $L^{[n]}$ against the virtual class. We conjecture a…

We study certain DT invariants arising from stable coherent sheaves in a nonsingular projective threefold supported on the members of a linear system of a fixed line bundle. When the canonical bundle of the threefold satisfies certain…

A CHL model is the quotient of $\mathrm{K3} \times E$ by an order $N$ automorphism which acts symplectically on the K3 surface and acts by shifting by an $N$-torsion point on the elliptic curve $E$. We conjecture that the primitive…

We discuss Donaldson-Thomas (DT) invariants of torsion sheaves with 2 dimensional support on a smooth projective surface in an ambient non-compact Calabi Yau fourfold given by the total space of a rank 2 bundle on the surface. We prove that…

In this paper, we investigate Keller's deformed Calabi--Yau completion of the derived category of coherent sheaves on a smooth variety. In particular, for an $n$-dimensional smooth variety $Y$, we describe the derived category of the total…

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 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…

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 work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth…

We solve the $K$-theoretically refined Donaldson-Thomas theory of local curves. Our results avoid degeneration techniques, but rather exploit direct localisation methods to reduce the refined Donaldson-Thomas partition function to the…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal sheaves on $X$ relative to $D$. These moduli spaces are compactified by studying…

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…

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 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 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.