On a conjecture about Higgs bundles for rank 2 and some inequalities
Algebraic Geometry
2024-12-31 v3
Abstract
We briefly review an open conjecture about Higgs bundles that are semistable with after pulling back to any curve, and prove it in the rank 2 case. We also prove a set of inequalities holding for H-nef Higgs bundles that generalize some of the Fulton-Lazarsfeld inequalities for numerically effective vector bundles.
Cite
@article{arxiv.2208.10554,
title = {On a conjecture about Higgs bundles for rank 2 and some inequalities},
author = {Ugo Bruzzo and Beatriz Graña Otero and Daniel Hernández Ruipérez},
journal= {arXiv preprint arXiv:2208.10554},
year = {2024}
}
Comments
13 pages. v2: 14 pages. Some results have been strengthened and the exposition has been reorganized. v3: minor changes, final version to appear in Mediterranean J. Math