Quadric bundles applied to non-maximal Higgs bundles

TL;DR

This paper surveys the moduli spaces of rank 2 quadric bundles over Riemann surfaces, highlighting their connection to non-maximal Higgs bundles and representations of the fundamental group in Sp(4,R).

Contribution

It provides a comprehensive overview of quadric bundles and their role in understanding non-maximal Higgs bundles and related moduli spaces.

Findings

Descriptions of moduli spaces of rank 2 quadric bundles

Connections between quadric bundles and non-maximal Higgs bundles

Relations to representations of the fundamental group in Sp(4,R)

Abstract

We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur through the study of the connected components of the moduli spaces of Higgs bundles over X for the real symplectic group Sp(4,R), with non-maximal Toledo invariant. Hence they are also related with the moduli space of representations of $\pi_1(X)$ in Sp(4,R). We explain this motivation in some detail.