Extension Phenomena for Holomorphic Geometric Structures

TL;DR

This paper investigates the extension properties of holomorphic geometric structures, showing that certain complex analytic G-structures and Cartan geometries cannot develop singularities of codimension two or higher.

Contribution

It establishes fundamental limitations on the singularity formation of holomorphic geometric structures, extending understanding of their extension phenomena.

Findings

Complex analytic G-structures cannot have codimension 2 or higher singularities.

Cartan geometries also exhibit similar extension restrictions.

Provides theoretical insights into the structure of holomorphic geometric objects.

Abstract

The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.