Stable Higgs bundles on compact Gauduchon manifolds

Details Stable Higgs bundles on compact Gauduchon manifolds Stable Higgs bundles on compact Gauduchon manifolds

2010-11-15

arxiv.org/abs/1011.3353v1

Mathematics

Algebraic Geometry

Comptes Rendus Mathematique (to appear)

Scientific paper

Let $M$ be a compact complex manifold equipped with a Gauduchon metric. If $TM$ is holomorphically trivial, and (V, \theta) is a stable SL(r,{\mathbb C})-Higgs bundle on $M$, then we show that $\theta= 0$. We show that the correspondence between Higgs bundles and representations of the fundamental group for a compact Kaehler manifold does not extend to compact Gauduchon manifolds. This is done by applying the above result to G/\Gamma, where $\Gamma$ is a discrete torsionfree cocompact subgroup of a complex semisimple group $G$.

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