Rank two quadratic pairs and surface group representations

Abstract

Let $X$ be a compact Riemann surface. A quadratic pair on $X$ consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that the moduli spaces of quadratic pairs of rank 2 are connected under some constraints on their topological invariants. As an application of our results we determine the connected components of the ${\mathrm{SO}}_0(2,3)$-character variety of $X$.

37 pages, 1 figure

References in corpus (1)

• The singular fibre of the Hitchin map

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