Parabolic Hitchin connection

TL;DR

This paper develops an algebraic geometric approach to constructing the Hitchin connection in the context of parabolic bundles, utilizing Hecke modifications and line bundle decompositions.

Contribution

It introduces a novel algebro-geometric construction of the parabolic Hitchin connection, including a decomposition formula for relevant line bundles.

Findings

Constructed a Hitchin connection on the moduli space of parabolic bundles.

Provided a decomposition formula for the parabolic determinant line bundle.

Extended the construction to vector bundles with fixed non-trivial determinants.

Abstract

In this paper, we present an algebro-geometric construction of the Hitchin connection in the parabolic setting for a fixed determinant line bundle. Our strategy is based on Hecke modifications, where we provide a decomposition formula for the parabolic determinant line bundle and the canonical line bundle of the moduli space of parabolic bundles. As a special case, we construct a Hitchin connection on the moduli space of vector bundles with fixed non-trivial determinant.