Locally Homogeneous Holomorphic Geometric Structures on Projective Varieties

TL;DR

This paper classifies subvarieties of smooth projective varieties that admit holomorphic locally homogeneous structures modeled on a homogeneous algebraic variety, identifying which subvarieties develop to the model.

Contribution

It provides a complete characterization of subvarieties developing to the model in the context of holomorphic locally homogeneous structures on projective varieties.

Findings

Identifies all subvarieties developing to the model.

Provides criteria for development of subvarieties.

Classifies structures on smooth projective varieties.

Abstract

For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.