Lectures on deformations of complex manifolds

TL;DR

This paper provides an accessible introduction to deformation theory of compact complex manifolds, covering foundational concepts and recent developments, aimed at non-expert PhD students.

Contribution

It offers a self-contained, user-friendly overview of extended deformation theory specifically for compact complex manifolds, including recent unpublished results.

Findings

Introduction to deformation theory concepts

Recent results in extended deformation theory

Applicability to broader deformation problems

Abstract

This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD student to deformations of compact complex manifolds, from the very beginning to some recent (i.e. at that time not yet published) results. The goal of these lectures is to give a soft introduction to extended deformation theory. In view of the aim (and the hope) of keeping this paper selfcontained, user friendly and with a tolerating number of pages, we consider only deformations of compact complex manifolds. Anyhow, most part of the formalism and of the results that we prove here will apply to many other deformation problems.