Cohomology and Obstructions I: Geometry of formal Kuranishi theory

TL;DR

This paper explores the role of cohomology in obstructing deformations of compact Kähler manifolds and their submanifolds, unifying various known results in deformation theory.

Contribution

It extends and unifies existing results on deformation obstructions in Kähler geometry, focusing on the geometry of formal Kuranishi theory.

Findings

Ambient cohomology annihilates obstructions in deformation problems

Unified framework for deformations of manifolds and submanifolds

Extension of classical results in Kähler deformation theory

Abstract

The principle "ambient cohomology of a Kaehler manifold annihilates obstructions" has been known and exploited since pioneering work of Kodaira. This paper extends and unifies many known results in two contexts, abstract deformations of compact Kaehler manifolds and deformations of submanifolds within a given deformation of the ambient manifold.