Generalized Bogomolov Inequalities
Algebraic Geometry
2026-05-05 v2
Abstract
We introduce the notion of a Hodge-Riemann pair of cohomology classes that generalizes the classical Hodge-Riemann bilinear relations, and the notion of a Bogomolov pair of cohomology classes that generalizes the Bogomolov inequality for semistable sheaves. We conjecture that every Hodge-Riemann pair is a Bogomolov pair, and prove various cases of this conjecture. As an application we get new results concerning boundedness of semistable sheaves.
Cite
@article{arxiv.2510.04663,
title = {Generalized Bogomolov Inequalities},
author = {Mihai Pavel and Julius Ross and Matei Toma},
journal= {arXiv preprint arXiv:2510.04663},
year = {2026}
}
Comments
32 pages. v2: Corrected Proposition 6.1 and its corollaries; we thank Ziquan Zhuang for pointing out an error in the previous proof of the proposition