Quadric bundles and their moduli spaces

TL;DR

This paper studies the moduli spaces of quadric bundles on Riemann surfaces, generalizing orthogonal bundles, and explores their properties especially in rank 2, with implications for representation theory.

Contribution

It establishes foundational results on the moduli spaces of quadric bundles of any rank and surveys advanced findings specifically for rank 2 cases.

Findings

Basic properties of moduli spaces of quadric bundles are established.

Connections between quadric bundles and representations of surface groups are discussed.

Survey of deeper results in the rank 2 case provides insights into their structure.

Abstract

Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric bundles over X of arbitrary rank and then survey deeper results in the rank 2 case.