Related papers: Structures in genus-zero relative Gromov--Witten t…

We study the Abramovich--Vistoli moduli space of genus zero orbifold stable maps to [Sym^2 P^2], the stack symmetric square of P^2. This compactifies the moduli space of stable maps from hyperelliptic curves to P^2, and we show that all…

We present a method of computing genus zero two-point descendant Gromov-Witten invariants via one-point invariants. We apply our method to recover some of calculations of Zinger and Popa-Zinger, as well as to obtain new calculations of…

Using the global Kuranishi charts constructed in \cite{HS22}, we define gravitational descendants and equivariant Gromov-Witten invariants for general symplectic manifolds. We prove that that these invariants, equivariant and…

We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions of a system of nonlinear first order elliptic partial differential equations in the ambient symplectic manifold. The symplectic manifold carries a…

The ring structure of Lian-Zuckerman states for $(q,p)$ minimal models coupled to gravity is shown to be ${\cal R}={\cal R}_0\otimes {\bf C} [w,w^{-1}]$ where ${\cal R}_0$ is the ring of ghost number zero operators generated by two elements…

There is a set of remarkable physical predictions for the structure of BCOV's higher genus B-model of mirror quintic 3-folds which can be viewed as conjectures for the Gromov-Witten theory of quintic 3-folds. They are (i) Yamaguchi--Yau's…

The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a…

This paper proposes a framework to show that the Fukaya category of a symplectic manifold $X$ determines the open Gromov-Witten invariants of Lagrangians $L \subset X$. We associate to an object in an $A_\infty$-category an extension of the…

The usual Gromov-Witten invariants are zero for K\"{a}hler surfaces with $p_g\geq 1$. In this paper we use analytic methods to define Family Gromov-Witten Invariants for K\"{a}hler surfaces. We prove that these are well-defined invariants…

We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…

We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of…

We discuss some properties of the relative Gromov--Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley's sextactic conics to any smooth plane curve $Y$. In particular, we…

We study genus 1 Gromov-Witten invariants of Fano complete intersections in the projective spaces. Among other things, we show a reconstruction theorem for genus 1 invariants with only ambient insertions, and compute the genus 1 invariants…

We make precise conjectures relating the genus zero Gromov-Witten theory of a nonabelian GIT quotient X//G to that of the associated abelian quotient X//T by a maximal torus T in G.These conjectures imply in particular closed formulas for…

We show that the generating functions of Gromov--Witten invariants with ancestors are invariant under a simple flop, for all genera, after an analytic continuation in the extended K\"ahler moduli space. This is a sequel to [LLW].

We give an alternate proof of the integrality conjecture of genus zero Gopakumar-Vafa type invariants on semi-positive varieties using algebraic geometry. The main technique is to relate Gopakumar-Vafa type invariants to quantum…

A scheme for solving quasiclassical string equations is developped to prove that genus-zero Whitham hierarchies describe the deformations of planar domains determined by rational conformal maps. This property is applied in normal matrix…

We study the structure of the higher genus Gromov-Witten theory of the total space $K\mathbb{P}^{n-1}$ of the canonical bundle of the projective space $\mathbb{P}^{n-1}$. We prove the finite generation property for the Gromov-Witten…

The construction of manifold structures and fundamental classes on the (compactified) moduli spaces appearing in Gromov-Witten theory is a long-standing problem. Up until recently, most successful approaches involved the imposition of…

We prove a quantum version of Kalkman's wall-crossing formula comparing Gromov-Witten invariants on geometric invariant theory (git) quotients related by a change in polarization. The wall-crossing terms are gauged Gromov-Witten invariants…