Restricting Higgs bundles to curves
Algebraic Geometry
2016-07-12 v3
Abstract
We determine some classes of varieties X - that include the varieties with numerically effective tangent bundle - satisfying the following property: if E is a Higgs bundle such that f*E is semistable for any morphism f from a smooth projective curve to X, then E is slope semistable and the discriminant of E is zero in H4(X,R). We also characterize some classes of varieties such that the underlying vector bundle of a slope semistable Higgs bundle is always slope semistable.
Cite
@article{arxiv.1310.2099,
title = {Restricting Higgs bundles to curves},
author = {Ugo Bruzzo and Alessio Lo Giudice},
journal= {arXiv preprint arXiv:1310.2099},
year = {2016}
}
Comments
11 pages. v2: 12 pages, final version to appear in Asian J. Math