Rank two quadratic pairs and surface group representations

Details Rank two quadratic pairs and surface group representations Rank two quadratic pairs and surface group representations

2011-06-09

arxiv.org/abs/1106.1766v1

Mathematics

Algebraic Geometry

37 pages, 1 figure

Scientific paper

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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