Related papers: Quivers and curves in higher dimension

We prove that genus zero Gromov--Witten invariants of a smooth scheme relative to a smooth divisor coincide with genus zero orbifold Gromov--Witten invariants of an appropriate root stack construction along the divisor.

We provide a transformation formula of non-commutative Donaldson-Thomas invariants under a composition of mutations. Consequently, we get a description of a composition of cluster transformations in terms of quiver Grassmannians. As an…

We apply the method of orbit harmonics to the set of break divisors and orientable divisors on graphs to obtain the central and external zonotopal algebras respectively. We then relate a construction of Efimov in the context of…

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 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…

In this note, genus zero Gromov-Witten invariants are reviewed and then applied in some examples of dimension four and six. It is also proved that the use of genus zero Gromov-Witten invariants in the class of embedded $J$-holomorphic…

We propose a conjecture that relates some local Gromov-Witten invariants of some crepant resolutions of Calabi-Yau 3-folds with isolated singularities with some Donaldson-Thomas type invariants of the moduli spaces of representations of…

Given a smooth projective variety $X$ and a smooth nef divisor $D$, we identify genus zero relative Gromov--Witten invariants of $(X,D)$ with $(n+1)$ relative markings with genus zero orbifold Gromov--Witten invariants of multi-root stacks…

This paper is a continuation of author's previous work arXiv:1911.07949, where we defined Donaldson-Thomas invariants of quantum Fermat threefolds. In this paper, we study the generic quantum Fermat threefold. We give explicit local models…

A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to…

We compute Gromov-Witten (GW) and Donaldson-Thomas (DT) invariants (and also descendant invariants) for local CY 4-folds over Fano 3-folds, V_5 and V_22 up to degree 3. We use torus localization for GW invariants computation, and use…

We review the recent proof of the N.Takahashi's conjecture on genus $0$ Gromov-Witten invariants of $(\mathbb{P}^2, E)$, where $E$ is a smooth cubic curve in the complex projective plane $\mathbb{P}^2$. The main idea is the use of the…

The present article is the first in a series whose ultimate goal is to prove the Kotschick-Morgan conjecture concerning the wall-crossing formula for the Donaldson invariants of a four-manifold with b^+ = 1. The conjecture asserts that the…

In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations…

We propose two conjectural relationships between the equivariant Gromov-Witten invariants of the resolved conifold under diagonal and anti-diagonal actions and the Gromov-Witten invariants of $\mathbb{P}^1$, and verify their validity in…

In a recent paper, we obtained a WDVV-type relation for real genus 0 Gromov-Witten invariants with conjugate pairs of insertions; it specializes to a complete recursion in the case of odd-dimensional projective spaces. This note provides…

We give more precise statements of Fock-Goncharov duality conjecture for cluster varieties parametrizing ${\rm SL}_{2}/{\rm PGL}_{2}$-local systems on the once punctured torus. Then we prove these statements. Along the way, using distinct…

We use the hyperK\"aler geometry define an disc-counting invariants with deformable boundary condition on hyperK\"ahler manifolds. Unlike the reduced Gromov-Witten invariants, these invariants can have non-trivial wall-crossing phenomenon…

We reformulate Kontsevich-Soibelman wall-crossing formulae for 4d $\mathcal{N}=2$ class $\mathcal{S}$ theories and corresponding BPS quivers, including those of wild type, as identities for generating series of symmetric quivers that…

We discuss the GW/DT correspondence for 3-folds in both the absolute and relative cases. Descendents in Gromov-Witten theory are conjectured to be equivalent to Chern characters of the universal sheaf in Donaldson-Thomas theory. Relative…