Deformations of cohesive modules on compact complex manifolds

TL;DR

This paper develops a deformation theory for cohesive modules on compact complex manifolds, generalizing existing theories for vector bundles and sheaves, and introduces Kuranishi maps and obstruction theory.

Contribution

It extends deformation theory to cohesive modules, providing new tools like Kuranishi maps and examples of unobstructed deformations.

Findings

Established a deformation framework for cohesive modules.

Developed Kuranishi maps and obstruction theory.

Provided examples of unobstructed deformations.

Abstract

Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This generalizes the deformation theory of holomorphic vector bundles and coherent sheaves. We also develop the theory of Kuranishi maps and obstructions of deformations of cohesive modules and give some examples of unobstructed deformations.