Extensions of Higgs bundles (Q1850267)

Here the authors prove a Hitchin-Kobayashi correspondence (i.e. the equivalence of \(\alpha\)-(poly)stability, \(\alpha\) a real negative parameter, and the existence of an \(\alpha\)HHE metric) for extensions of Higgs bundles on a compact Kähler manifold. They use an approach introduced by Simpson. They also extend to Higgs bundles the construction of Bott-Chern forms and use the gauge-theoretic equations to deduce Bogomolov-type inequalities on the Chern classes of stable Higgs extensions.