A Higgs bundle on a Hermitian symmetric space |
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Authors: | Indranil Biswas Oscar García-Prada |
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Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400005, India;(2) Departamento de Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 121, Madrid, 28006, Spain |
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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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Keywords: | Hermitian symmetric space Higgs bundle Flat connection |
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