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Related papers: Open Gromov-Witten theory without Obstruction

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We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the…

Algebraic Geometry · Mathematics 2016-01-13 Edward Frenkel , Constantin Teleman , A. J. Tolland

New relations among the genus-zero Gromov-Witten invariants of a complex projective manifold $X$ are exhibited. When the cohomology of $X$ is generated by divisor classes and classes ``with vanishing one-point invariants,'' the relations…

Algebraic Geometry · Mathematics 2007-05-23 Aaron Bertram , Holger P. Kley

We give a definition of all-genus reduced Gromov-Witten invariants of symplectic manifolds by using effectively supported multivalued perturbations on derived orbifold/Kuranishi charts, which bypasses the hard analytical result of sharp…

Symplectic Geometry · Mathematics 2026-04-16 Guangbo Xu

This paper describes the structure of the moduli space of holomorphic curves and constructs Gromov Witten invariants in the category of exploded manifolds. This includes defining Gromov Witten invariants relative to normal crossing divisors…

Symplectic Geometry · Mathematics 2011-02-02 Brett Parker

In this note we show how Kontsevich-Soibelman algebra arise naturally in Open Gromov-Witten theory for not compact geometries.

Symplectic Geometry · Mathematics 2024-12-06 Vito Iacovino

In \cite{TY18}, higher genus Gromov--Witten invariants of the stack of $r$-th roots of a smooth projective variety $X$ along a smooth divisor $D$ are shown to be polynomials in $r$. In this paper we study the degrees and coefficients of…

Algebraic Geometry · Mathematics 2022-01-25 Hsian-Hua Tseng , Fenglong You

We describe properties of the previously constructed all-genus real Gromov-Witten theory in the style of Kontsevich-Manin's axioms and other classical equations and reconstruction results of complex Gromov-Witten theory.

Algebraic Geometry · Mathematics 2023-11-21 Penka Georgieva , Aleksey Zinger

The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed…

Algebraic Geometry · Mathematics 2007-05-23 Charles Cadman

We propose a conjectural explicit formula of generating series of a new type for Gromov--Witten invariants of $\mathbb{P}^1$ of all degrees in full genera.

Algebraic Geometry · Mathematics 2025-05-23 Boris Dubrovin , Di Yang

The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference…

Algebraic Geometry · Mathematics 2014-07-07 Simon Rose

A bicyclic pair is a smooth surface equipped with a pair of smooth divisors intersecting in two reduced points. Resolutions of self-nodal curves constitute an important special case. We investigate the logarithmic Gromov-Witten theory of…

Algebraic Geometry · Mathematics 2025-07-08 Michel van Garrel , Navid Nabijou , Yannik Schuler

The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…

Algebraic Geometry · Mathematics 2017-08-17 Aleksey Zinger

This paper classifies separated bounding pairs for Lagrangian submanifolds that are homologically trivial inside the ambient space, under the assumption that restriction on cohomology from the ambient space to the Lagrangian is surjective.…

Symplectic Geometry · Mathematics 2023-12-01 Sara B. Tukachinsky

For a symplectic manifold with an anti-symplectic involution having non-empty fixed locus, we construct a model of the moduli space of real sphere maps out of moduli spaces of decorated disk maps and give an explicit expression for its…

Symplectic Geometry · Mathematics 2015-10-29 Penka Georgieva

In this paper, we study relations among known universal equations for Gromov-Witten invariants at genus 1 and 2.

Differential Geometry · Mathematics 2007-05-23 Xiaobo Liu

We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivariant theory is governed by the 2-Toda hierarchy of Ueno and…

Algebraic Geometry · Mathematics 2007-05-23 Andrei Okounkov , Rahul Pandharipande

The orientability problem in real Gromov-Witten theory is one of the fundamental hurdles to enumerating real curves. In this paper, we describe topological conditions on the target manifold which ensure that the uncompactified moduli spaces…

Symplectic Geometry · Mathematics 2013-11-27 Penka Georgieva , Aleksey Zinger

The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working…

Symplectic Geometry · Mathematics 2018-02-27 Penka Georgieva , Aleksey Zinger

In the first part of the paper, we give an explicit algorithm to compute the (genus zero) Gromov-Witten invariants of blow-ups of an arbitrary convex projective variety in some points if one knows the Gromov-Witten invariants of the…

Algebraic Geometry · Mathematics 2009-09-25 Andreas Gathmann

Relative orbifold Gromov-Witten theory is set-up and the degeneration formula is given.

Symplectic Geometry · Mathematics 2025-01-17 Bohui Chen , An-Min Li , Shanzhong Sun , Guosong Zhao