A note on the Chern classes of stable Higgs bundles on surfaces

Yoichi Miyaoka

U. Tokyo, Japan

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Abstract

We construct a rank 4 stable Higgs bundle for which the Bogomolov inequality breaks down. From this example, we derive a non-trivial family of stable Higgs bundles of rank 4 with Simpson's theorem implies that this gives a non-trivial deformation of indecomposable representations of the fundamental group of the base surface.