Invariants of stable quasimaps with fields

TL;DR

This paper constructs a moduli space of quasimaps with P fields for smooth hypersurfaces, establishing a cycle-level identity that generalizes Gromov-Witten invariants to quasimap invariants.

Contribution

It introduces a new LG moduli space with P fields for hypersurfaces and proves its virtual class matches that of quasimaps to the hypersurface, extending previous identities.

Findings

Virtual fundamental class constructed via cosection localization

Cycle-level identity between quasimap and Gromov-Witten invariants

Generalization to arbitrary smooth hypersurfaces

Abstract

For an arbitrary smooth hypersurface X in a projective space, we construct its LG moduli of quasimaps with P fields. Apply Kiem-Li's cosection localization we obtain a virtual fundamental class. We show the class coincides, up to sign, with that of moduli of quasimaps to X. This generalizes Chang-Li's numerical identity to the cycle level, and from Gromov Witten invariants to quasimap invariants.