Deformations of cohesive modules on compact complex manifolds

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.