Cohomologies of Landau-Ginzburg models

TL;DR

This paper investigates various cohomology theories related to Landau-Ginzburg models, focusing on their properties and interrelations, especially in the context of complete complex manifolds.

Contribution

It establishes isomorphisms and self-duality of different cohomologies associated with Koszul complexes in Landau-Ginzburg models for complete manifolds.

Findings

Cohomologies are isomorphic when the manifold is complete

Cohomologies exhibit self-duality in this setting

Provides a unified understanding of Landau-Ginzburg cohomologies

Abstract

Let V be a holomorphic bundle over a complex manifold M, and s be a holomorphic section of V. We study different types of cohomology associated to the Koszul complex induced by s. When M is complete, these cohomologies are isomorphic to each other and have self duality.