Related papers: Quivers and curves in higher dimension

We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm,…

Given a covering of a quiver (with potential), we show that the associated Bridgeland stability scattering diagrams are related by a restriction operation under the assumption of admitting a nice grading. We apply this to quivers with…

For each positive rational number epsilon, the theory of epsilon-stable quasimaps to certain GIT quotients W//G developed in arXiv:1106.3724[math.AG] gives rise to a Cohomological Field Theory. Furthermore, there is an asymptotic theory…

We consider the moduli space of the McKay quiver representations associated to the binary polyhedral groups G < SU(2) < SU(3). The derived category of such representations is equivalent to the derived category of coherent sheaves on the…

We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for…

We study the Gromov-Witten and Donaldson-Thomas correspondence conjectured in [MNOP1, MNOP2], for trivial elliptic fibrations. In particular, we verify the Gromov-Witten and Donaldson-Thomas correspondence for primary fields when the…

This is the first in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology $QH_G(X)$ of a smooth complex projective variety X with the action of a connected complex reductive…

We study K-theoretic Gromov--Witten invariants of projective hypersurfaces using a virtual localization formula under finite group actions. In particular, it provides all K-theoretic Gromov--Witten invariants of the quintic threefold modulo…

We define Gromov-Witten classes and invariants of smooth proper tame Deligne-Mumford stacks of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth proper…

We offer a pedestrian level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In non-trivial situations,…

In arXiv:0907.3784, we introduced a variant of non-commutative Donaldson-Thomas theory in a combinatorial way, which is related with topological vertex by a wall-crossing phenomenon. In this paper, we (1) provide an alternative definition…

We extend the definition of relative Gromov--Witten invariants with negative contact orders to all genera. Then we show that relative Gromov--Witten theory forms a partial CohFT. Some cycle relations on the moduli space of stable maps are…

A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…

We introduce a holomorphic version of Weinstein's symplectic category, in which objects are holomorphic symplectic manifolds, and morphisms are holomorphic lagrangian correspondences. We then extend this category to log schemes, and prove…

We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these…

We describe a correspondence between the virtual number of torsion free sheaves locally free in codimension 3 on a Calabi-Yau 3-fold and the Gromov-Witten invariants counting rational curves in a family of orbifold blowups of the weighted…

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…

The Landau-Ginzburg/Calabi-Yau correspondence claims that the Gromov-Witten invariant of the quintic Calabi-Yau 3-fold should be related to the Fan-Jarvis-Ruan-Witten invariant of the associated Landau-Ginzburg model via wall crossings. In…

Splitting invariants describe how a plane curve "splits" by the pull-back under a Galois cover over the projective plane whose branch locus contains no component of the plane curve. They enable us to distinguish the embedded topology of…

We solve a conjecture of Morgan and Szabo (Embedded genus 2 surfaces in four-manifolds, Preprint) about the relationship of the basic classes of two four-manifolds $X_i$ of simple type with $b_1=0$, $b^+>1$, such that there are embedded…