Criterion for existence of a logarithmic connection on a principal bundle over a smooth complex projective variety

TL;DR

This paper establishes criteria for when a holomorphic principal G-bundle over a smooth complex projective variety admits a logarithmic connection singular along a divisor, advancing understanding of connections in complex geometry.

Contribution

It provides a new criterion for the existence of logarithmic connections on principal bundles over complex projective varieties.

Findings

Criteria for the existence of logarithmic connections

Application to principal G-bundles on complex varieties

Enhanced understanding of singular connections in algebraic geometry

Abstract

Let $X$ be a connected smooth complex projective variety of dimension $n \geq 1$. Let $D$ be a simple normal crossing divisor on $X$. Let $G$ be a connected complex Lie group, and $E_G$ a holomorphic principal $G$-bundle on $X$. In this article, we give criterion for existence of a logarithmic connection on $E_G$ singular along $D$.