Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic
arXiv:2210.08767 · doi:10.1515/crelle-2023-0101
Abstract
We prove Bogomolov's inequality on a normal projective variety in positive characteristic and we use it to show some new restriction theorems and a new boundedness result. Then we redefine Higgs sheaves on normal varieties and we prove restriction theorems and Bogomolov type inequalities for semistable logarithmic Higgs sheaves on some normal varieties in an arbitrary characteristic.
61 pages; v2: 67 pages, corrected errors in restriction theorems for semistability, corrected definitions in 1.2, rewritten Subsection 3.4; v3: 68 pages, some small corrections, added Corollary 3.17