Virtual cycles of stable (quasi)-maps with fields

TL;DR

This paper extends the theory of moduli spaces of p-fields to (quasi-)maps into complete intersections within smooth Deligne-Mumford stacks, establishing a link between their virtual cycles via cosection localization.

Contribution

It generalizes previous results to a broader setting of stacks and complete intersections, connecting virtual cycles of (quasi-)maps with p-fields through cosection localization.

Findings

Virtual cycle of stable (quasi-)maps can be recovered from p-fields.

Generalization to arbitrary smooth Deligne-Mumford stacks.

Establishes a cosection localized virtual cycle correspondence.

Abstract

We generalize the results of Chang-Li, Kim-Oh and Chang-Li on the moduli of $p$-fields to the setting of (quasi-)maps to complete intersections in arbitrary smooth Deligne-Mumford stacks with projective coarse moduli. In particular, we show that the virtual cycle of stable (quasi-)maps to a complete intersection can be recovered by the cosection localized virtual cycle of the moduli of $p$-fields of the ambient space.