A Hitchin connection on non abelian theta functions for parabolic G-bundles

TL;DR

This paper establishes a flat projective connection on nonabelian theta functions over moduli spaces of parabolic G-bundles, advancing understanding of geometric structures in algebraic geometry.

Contribution

It proves the existence of a flat projective connection on nonabelian theta functions for parabolic G-bundles, a novel result in the study of moduli spaces.

Findings

Existence of a flat projective connection proven

Applicable to moduli of semistable parabolic G-bundles

Enhances geometric understanding of nonabelian theta functions

Abstract

For a simple, simply connected, complex group G, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points.