Einstein-Hermitian connection on twisted Higgs bundles

Indranil Biswas; Tomas L. Gomez; Norbert Hoffmann; Amit Hogadi

Einstein-Hermitian connection on twisted Higgs bundles

Algebraic Geometry 2010-08-13 v1 Differential Geometry

Authors: Indranil Biswas , Tomas L. Gomez , Norbert Hoffmann , Amit Hogadi

Abstract

Let $X$ be a smooth projective variety over $\mathbb C$ . We prove that a twisted Higgs vector bundle $(\calE\, ,\theta)$ on $X$ admits an Einstein--Hermitian connection if and only if $(\calE\, ,\theta)$ is polystable. A similar result for twisted vector bundles (no Higgs fields) was proved by S. Wang in \cite{Wa}. Our approach is simpler.

Keywords

higgs bundle holomorphic vector bundles vector bundles

Cite

@article{arxiv.1008.2034,
  title  = {Einstein-Hermitian connection on twisted Higgs bundles},
  author = {Indranil Biswas and Tomas L. Gomez and Norbert Hoffmann and Amit Hogadi},
  journal= {arXiv preprint arXiv:1008.2034},
  year   = {2010}
}

Comments

To appear in Comptes rendus Mathematique

Einstein-Hermitian connection on twisted Higgs bundles

Abstract

Keywords

Cite

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