Semistable principal Higgs bundles
Algebraic Geometry
2008-10-20 v2
Abstract
We give a Miyaoka-type semistability criterion for principal Higgs G-bundles E on complex projective manifolds of any dimension, i.e., we prove that E is semistable and the second Chern class of its adjoint bundle vanishes if and only if certain line bundles, obtained from the characters of the parabolic subgroups of G, are numerically effective. We also give alternative characterizations in terms of a notion of numerical effectiveness of Higgs vector bundles we have recently introduced.
Cite
@article{arxiv.0809.3936,
title = {Semistable principal Higgs bundles},
author = {Ugo Bruzzo and Beatriz Grana Otero},
journal= {arXiv preprint arXiv:0809.3936},
year = {2008}
}
Comments
14 pages. v2: typos corrected, minor additions