Infinitesimal Deformations of Complex Manifolds and Vector Bundles

Abstract

In this chapter we study deformations, over Artin local rings, of manifolds and vector bundles. We follow a classical approach, similar to every standard introductory book in deformation theory. However, for later applications, we interpret all the involved deformation functors either as the exponential functor of a Lie algebra or as the functor associated with a semicosimplicial Lie algebra.