Geometry of Kodaira moduli spaces

TL;DR

This paper proves a general theorem on the existence of natural torsion-free affine connections on complete families of compact complex submanifolds, with applications to twistor theory.

Contribution

It introduces a new general theorem establishing conditions for natural affine connections on complex submanifold families, advancing geometric understanding.

Findings

Existence of torsion-free affine connections in specific geometric contexts

Applications to twistor theory demonstrate practical relevance

Provides a framework for studying moduli spaces of complex submanifolds

Abstract

A general theorem on the existence of natural torsion-free affine connections on a complete family of compact complex submanifolds in a complex manifold is proved. Applications to twistor theory are discussed.