The Lipman-Zariski conjecture in low genus
Algebraic Geometry
2021-05-07 v2 Commutative Algebra
Complex Variables
Abstract
We prove the Lipman-Zariski conjecture for complex surface singularities of genus one, and also for those of genus two whose link is not a rational homology sphere. As an application, we characterize complex -tori as the only normal compact complex surfaces whose smooth locus has trivial tangent bundle. We also deduce that all complex-projective surfaces with locally free and generically nef tangent sheaf are smooth, and we classify them.
Keywords
Cite
@article{arxiv.1801.05753,
title = {The Lipman-Zariski conjecture in low genus},
author = {Patrick Graf},
journal= {arXiv preprint arXiv:1801.05753},
year = {2021}
}
Comments
Published version is slightly shortened