A parabolic analog of a theorem of Beilinson and Schechtman

TL;DR

This paper derives an explicit formula for the Atiyah class of the parabolic determinant of cohomology line bundle on moduli spaces of parabolic G-bundles, extending previous work by Beilinson and Schechtman.

Contribution

It provides a new explicit formula for the Atiyah class in the context of parabolic G-bundles, generalizing earlier results.

Findings

Explicit formula for the Atiyah class of parabolic determinant line bundle

Generalization of Beilinson-Schechtman's theorem to parabolic bundles

Enhanced understanding of the geometry of moduli spaces of parabolic G-bundles

Abstract

For a simple, simply connected, complex group G, we prove an explicit formula to compute the Atiyah class of parabolic determinant of cohomology line bundle on the moduli space of parabolic $G$-bundles. This generalizes an earlier result of Beilinson-Schechtman.