Gromov-Witten Gauge Theory I

TL;DR

This paper develops a geometric framework for gauge-theoretic Gromov-Witten invariants by completing the stack of maps to quotient stacks, extending classical invariants to new algebraic geometric contexts.

Contribution

It introduces a geometric completion of the stack of maps to [point/GL(1)] and constructs gauge-theoretic analogues of Gromov-Witten invariants, generalizable to [X/GL(1)] for smooth proper varieties.

Findings

Constructed a geometric completion of the stack of maps to [point/GL(1)].

Defined gauge-theoretic analogues of Gromov-Witten invariants.

Outlined potential generalizations to quotient stacks [X/GL(1)].

Abstract

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 generalization of these invariants to the quotient stacks [X/GL(1)], where X is a smooth proper complex algebraic variety.