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 a 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 SO0(2, 3)-character variety of X.
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Members of VBAC (Vector Bundles on Algebraic Curves). Partially supported by CRUP through Acção Integrada Luso-Espanhola no.E-38/09 and by the FCT (Portugal) with EU (COMPETE) and national funds through the projects PTDC/MAT/099275/2008 and PTDC/MAT/098770/2008, and through Centro de Matemática da Universidade do Porto (PEst-C/MAT/UI0144/2011, Peter B. Gothen) and Centro de Matemática da Universidade de Trás-os-Montes e Alto Douro (PEst-OE/MAT/UI4080/2011, André G. Oliveira).
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Gothen, P.B., Oliveira, A.G. Rank two quadratic pairs and surface group representations. Geom Dedicata 161, 335–375 (2012). https://doi.org/10.1007/s10711-012-9709-1
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DOI: https://doi.org/10.1007/s10711-012-9709-1