Rank two quadratic pairs and surface group representations

Peter B. Gothen; André Oliveira

doi:10.1007/s10711-012-9709-1

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arXiv · 1106.1766

Rank two quadratic pairs and surface group representations

Peter B. Gothen·André Oliveira

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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 $X$.

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Peter B. Gothen, André Oliveira. 2011-06-09. Rank two quadratic pairs and surface group representations. https://doi.org/10.1007/s10711-012-9709-1

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