Fundamental Factorization of a GLSM, Part I: Construction

Understand

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.