%0 Journal Article
%T Semistability vs. nefness for (Higgs) vector bundles
%A U. Bruzzo
%A D. Hernandez Ruiperez
%J Mathematics
%D 2003
%I arXiv
%R 10.1016/j.difgeo.2005.12.007
%X According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.
%U http://arxiv.org/abs/math/0310040v3