Matrix factorizations for nonaffine LG-models

TL;DR

This paper introduces a new category of matrix factorizations for nonaffine Landau-Ginzburg models and establishes a functorial relationship with the triangulated category of singularities, proving equivalence in smooth cases.

Contribution

It defines a natural category of matrix factorizations for nonaffine LG-models and proves an equivalence with the singularity category when the total space is smooth.

Findings

Constructed a fully faithful functor from matrix factorizations to singularity categories.

Proved the functor is an equivalence for smooth total spaces.

Extended the theory of matrix factorizations to nonaffine LG-models.

Abstract

We propose a natural definition of a category of matrix factorizations for nonaffine Landau-Ginzburg models. For any LG-model we construct a fully faithful functor from the category of matrix factorizations defined in this way to the triangulated category of singularities of the corresponding fiber. We also show that this functor is an equivalence if the total space of the LG-model is smooth.