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A Higgs bundle on a Hermitian symmetric space

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Abstract

Let \(M := \Gamma\backslash G/K\) be the quotient of an irreducible Hermitian symmetric space G/K by a torsionfree cocompact lattice \(\Gamma\subset G\) . There is a natural flat principal G-bundle over the compact Kähler manifold M which is constructed from the principal Γ-bundle over M defined by the quotient map \(G/K\longrightarrow M\) . We construct the principal G-Higgs bundle over M corresponding to this flat G-bundle. This principal G-Higgs bundle is rigid if \({\rm dim}_\mathbb{C} M\,\geq\,2\) .

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400005, India

    Indranil Biswas

  2. Departamento de Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 121, Madrid, 28006, Spain

    Oscar García-Prada

Authors
  1. Indranil Biswas
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  2. Oscar García-Prada
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Correspondence to Indranil Biswas.

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Biswas, I., García-Prada, O. A Higgs bundle on a Hermitian symmetric space. Geom Dedicata 127, 87–98 (2007). https://doi.org/10.1007/s10711-007-9162-8

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  • DOI: https://doi.org/10.1007/s10711-007-9162-8

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