Moduli stacks of stable toric quasimaps

TL;DR

This paper introduces new modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties, generalizing existing constructions and connecting to Gromov-Witten theory.

Contribution

It constructs 'virtually smooth' compactifications of moduli spaces of stable toric quasimaps, extending Givental's compactifications and relating to stable quotient spaces.

Findings

New compactifications are constructed and shown to be 'virtually smooth'

The work generalizes Givental's compactifications with variable complex structures and markings

Discussion of invariants and their conjectural relation to Gromov-Witten theory

Abstract

We construct new "virtually smooth" modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by Marian, Oprea, and Pandharipande to compactify spaces of maps to Grassmannians. A brief discussion of the resulting invariants and their (conjectural) relation with Gromov-Witten theory is also included.