Semistability vs. nefness for (Higgs) vector bundles
Abstract
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.
Keywords
Cite
@article{arxiv.math/0310040,
title = {Semistability vs. nefness for (Higgs) vector bundles},
author = {U. Bruzzo and D. Hernandez Ruiperez},
journal= {arXiv preprint arXiv:math/0310040},
year = {2007}
}
Comments
Comments: 20 pages, Latex2e, no figures. v2 includes a generalization to complex projective manifolds of any dimension. To appear in Diff. Geom. Appl