Projectively flat KLT varieties
Algebraic Geometry
2022-01-10 v1 Complex Variables
Differential Geometry
Abstract
In the context of uniformisation problems, we study projective varieties with klt singularities whose cotangent sheaf admits a projectively flat structure over the smooth locus. Generalising work of Jahnke-Radloff, we show that torus quotients are the only klt varieties with semistable cotangent sheaf and extremal Chern classes. An analogous result for varieties with nef normalised cotangent sheaves follows.
Cite
@article{arxiv.2010.06878,
title = {Projectively flat KLT varieties},
author = {Daniel Greb and Stefan Kebekus and Thomas Peternell},
journal= {arXiv preprint arXiv:2010.06878},
year = {2022}
}