Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

TL;DR

This paper develops a method to compute equivariant Gromov-Witten invariants of algebraic GKM manifolds using virtual localization, expressing results in terms of Hodge integrals and GKM graph data.

Contribution

It introduces a novel approach to calculate Gromov-Witten invariants for non-compact GKM manifolds via virtual localization and GKM graph analysis.

Findings

Expresses invariants in terms of Hodge integrals and GKM graphs.

Applicable to non-compact algebraic GKM manifolds.

Provides a systematic computational framework.

Abstract

An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.