A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface

  • Indranil Biswas

    School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Bombay 400005 India
A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface cover
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Abstract

Let be a holomorphic principal -bundle over a compact connected Riemann surface, where is a connected reductive affine algebraic group defined over , such that admits a holomorphic connection. Take any , where is the adjoint vector bundle for , such that the conjugacy class , is independent of . We give a sufficient condition for the existence of a holomorphic connection on such that is flat with respect to the induced connection on .

Cite this article

Indranil Biswas, A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface. Doc. Math. 18 (2013), pp. 111–120

DOI 10.4171/DM/393