Related papers: Quantum geometry, stability and modularity
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…
The Castelnuovo bound conjecture, which is proposed by physicists, predicts an effective vanishing result for Gopakumar-Vafa invariants of Calabi-Yau 3-folds of Picard number one. Previously, it is only known for a few cases and all the…
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 apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the $(0,1,2)$-dimensional part of…
We prove wall-crossing formula for categorical Donaldson-Thomas invariants on the resolved conifold, which categorifies Nagao-Nakajima wall-crossing formula for numerical DT invariants on it. The categorified Hall products are used to…
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…
We derive two multivariate generating functions for three-dimensional Young diagrams (also called plane partitions). The variables correspond to a colouring of the boxes according to a finite Abelian subgroup G of SO(3). We use the vertex…
The generalized Donaldson-Thomas invariants counting one dimensional semistable sheaves on Calabi-Yau 3-folds are conjectured to satisfy a certain multiple cover formula. This conjecture is equivalent to Pandharipande-Thomas's strong…
We begin the study of categorifications of Donaldson-Thomas invariants associated with Hilbert schemes of points on the three-dimensional affine space, which we call DT categories. The DT category is defined to be the category of matrix…
We study the problem of computing Gopakumar-Vafa invariants for multiparameter families of symmetric Calabi-Yau threefolds admitting flops to diffeomorphic manifolds. There are infinite Coxeter groups, generated by permutations and flops,…
We construct semiorthogonal decompositions of Donaldson-Thomas (DT) categories for reduced curve classes on local surfaces into products of quasi-BPS categories and Pandharipande-Thomas (PT) categories, giving a categorical analogue of the…
Our goal in this paper is to discuss a conjectural correspondence between enumerative geometry of curves in Calabi-Yau 5-folds $Z$ and 1-dimensional sheaves on 3-folds $X$ that are embedded in $Z$ as fixed points of certain…
We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces. These can be used to systematically construct elliptically and genus…
We survey the foundations for Donaldson-Thomas invariants for stable sheaves on algebraic threefolds with trivial canonical bundle, with emphasis on the case of abelian threefolds.
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.
On the affine space containing the space $\mathcal{S}$ of quantum states of finite-dimensional systems there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding relevant…
We construct a state-sum type invariant of smooth closed oriented $4$-manifolds out of a $G$-crossed braided spherical fusion category ($G$-BSFC) for $G$ a finite group. The construction can be extended to obtain a $(3+1)$-dimensional…
F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function $Z_{top}$ of the refined topological string on these…
We compute the reduced genus 1 Gromov-Witten invariants of Calabi-Yau hypersurfaces. As a consequence, we confirm the 1993 Bershadsky-Cecotti Ooguri-Vafa (BCOV) prediction for the standard genus 1 GW-invariants of a quintic threefold. We…
Motivated by previous computations of Y. Cao, M. Kool and the author, we propose square roots and sign rules for the vertex and edge terms that compute Donaldson-Thomas invariants of a toric Calabi-Yau 4-fold, and prove that they are…