A Note on Parabolic Bundles on Nodal Curves

TL;DR

This paper extends the Mehta-Seshadri correspondence, which links unitary representations and stable parabolic bundles, to irreducible projective curves with nodal singularities, broadening its applicability.

Contribution

It generalizes the Mehta-Seshadri correspondence to include irreducible projective curves with nodes, expanding the theory to singular algebraic curves.

Findings

Establishes the correspondence for nodal curves.

Shows stability conditions extend to singular curves.

Provides a framework for analyzing parabolic bundles on singular curves.

Abstract

Mehta and Seshadri have proved that the set of equivalence classes of irreducible unitary representations of the fundamental group of a punctured compact Riemann surface, can be identified with equivalence classes of stable parabolic bundles of parabolic degree zero on the compact Riemann surface. In this note, we discuss the Mehta-Seshadri correspondence over an irreducible projective curve with at most nodes as singularities.