Fundamental Factorization of a GLSM, Part I: Construction

TL;DR

This paper introduces a new framework for enumerative invariants in hybrid GLSMs, unifying Gromov-Witten and FJRW invariants through a fundamental factorization and Fourier-Mukai transform.

Contribution

It constructs a fundamental factorization on the moduli space of Landau-Ginzburg maps, unifying existing invariants within a new theoretical framework.

Findings

Recoveries of Gromov-Witten and FJRW invariants in special cases

Construction of a fundamental factorization supported on the moduli space

Definition of invariants via a Fourier-Mukai transform on Hochschild homology

Abstract

We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk-Vaintrob. The invariants are defined by constructing a "fundamental factorization" supported on the moduli space of Landau-Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier-Mukai transform; the associated map on Hochschild homology defines our theory.