Quadric bundles applied to non-maximal Higgs bundles

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.

To appear in the special volume of Travaux Mathématiques dedicated to the GEOQUANT 2015 Conference held at the ICMAT, Madrid; 15 pages

References in corpus (1)

• The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations