English

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 2\ge 2 without using any restriction theorems.

Keywords

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

R2 v1 2026-06-24T03:57:41.233Z