On boundedness of semistable sheaves
Algebraic Geometry
2023-01-31 v2
Abstract
We give a new simple proof of boundedness of the family of semistable sheaves with fixed numerical invariants on a fixed smooth projective variety. In characteristic zero our method gives a quick proof of Bogomolov's inequality for semistable sheaves on a smooth projective variety of any dimension without using any restriction theorems.
Cite
@article{arxiv.2107.03125,
title = {On boundedness of semistable sheaves},
author = {Adrian Langer},
journal= {arXiv preprint arXiv:2107.03125},
year = {2023}
}
Comments
v2: 12 pages, many changes improving readibility of the paper and making it more self-contained; added new restriction Theorem 3.7 on the projective space; added Appendix containing author's variant of proof of Bogomolov's inequality