# Serre Duality for the Cohomology of Landau-Ginzburg models

## TL;DR

This paper extends Serre duality to the cohomology of Landau-Ginzburg models, specifically focusing on the Koszul complex associated with holomorphic bundles and sections over complex manifolds.

## Contribution

It proves a generalized Serre duality theorem for the cohomology of Koszul complexes in Landau-Ginzburg models, advancing the understanding of their duality properties.

## Key findings

- Established a duality theorem for Koszul complex cohomology
- Extended Serre duality to Landau-Ginzburg model context
- Provided mathematical framework for future research in complex geometry

## Abstract

Let V and F be holomorphic bundles over a complex manifold M, and s be a holomorphic section of V. We study the cohomology associated to the Koszul complex induced by s, and prove a generalized Serre duality theorem for them.