Numerically flat Higgs vector bundles
Algebraic Geometry
2007-08-20 v1
Abstract
After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.
Cite
@article{arxiv.math/0603509,
title = {Numerically flat Higgs vector bundles},
author = {Ugo Bruzzo and Beatriz Graña Otero},
journal= {arXiv preprint arXiv:math/0603509},
year = {2007}
}
Comments
11 pages