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Rank two quadratic pairs and surface group representations

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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 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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Authors and Affiliations

  1. Faculdade de Ciências, Centro de Matemática da Universidade do Porto, Universidade do Porto, Rua do Campo Alegre, 4169-007, Porto, Portugal

    Peter B. Gothen

  2. Centro de Matemática, Universidade de Trás-os-Montes e Alto Douro, Quinta dos Prados, Apartado 1013, 5000-911, Vila Real, Portugal

    André G. Oliveira

Authors
  1. Peter B. Gothen
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  2. André G. Oliveira
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Correspondence to Peter B. Gothen.

Additional information

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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