A gauge theoretic aspect of parabolic bundles over real curves

TL;DR

This paper explores the gauge theory framework for real and quaternionic parabolic bundles over real curves, analyzing the structure of their moduli spaces and gauge orbits in a complex geometric setting.

Contribution

It introduces a gauge-theoretic perspective on real and quaternionic parabolic bundles, connecting gauge orbits with real points of moduli spaces on Riemann surfaces.

Findings

Characterization of gauge orbits for real and quaternionic structures

Identification of gauge-theoretic quotients within real points of moduli spaces

Analysis of the orbit space structure under gauge group actions

Abstract

In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve $(X, \sigma_X)$, where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed real or quaternionic structure on a smooth parabolic bundle, we examine the orbits space of real or quaternionic connection under the appropriate gauge group. The corresponding gauge-theoretic quotients sit inside the real points of the moduli of holomorphic parabolic bundles having a fixed parabolic type on a compact Riemann surface $X$.