Holomorphic Cartan geometries on uniruled surfaces

TL;DR

This paper classifies holomorphic Cartan geometries on compact complex curves and certain surfaces, providing a comprehensive understanding of their structure in these settings.

Contribution

It offers a complete classification of holomorphic Cartan geometries on all compact complex curves and on surfaces containing rational curves, filling a gap in geometric theory.

Findings

Classification of geometries on complex curves

Classification on surfaces with rational curves

Enhanced understanding of geometric structures on complex surfaces

Abstract

We classify holomorphic Cartan geometries on every compact complex curve, and on every compact complex surface which contains a rational curve.