An overview on curve semistable and numerically flat Higgs bundles
Algebraic Geometry
2025-12-30 v1
Abstract
After recalling the basic notions concerning Higgs-Grassmannian schemes, I review how these latter can be used to define generalisations of the notion of positivity conditions, such as numerically flatness, which "feel" the Higgs field. Then I prove several properties of Higgs bundles, over smooth projective varieties defined over an algebraically closed field of characteristic , satisfying these conditions. Finally, I discuss how one can relate them to semistability of the so-called "curve semistable" Higgs bundles.
Cite
@article{arxiv.2512.23529,
title = {An overview on curve semistable and numerically flat Higgs bundles},
author = {Armando Capasso},
journal= {arXiv preprint arXiv:2512.23529},
year = {2025}
}
Comments
11 pages