Einstein-Hermitian connection on twisted Higgs bundles

Details Einstein-Hermitian connection on twisted Higgs bundles Einstein-Hermitian connection on twisted Higgs bundles

2010-08-12

arxiv.org/abs/1008.2034v1

Mathematics

Algebraic Geometry

To appear in Comptes rendus Mathematique

Scientific paper

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.

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