The Lipman–Zariski Conjecture in Low Genus-Reference-Cited by-同舟云学术

The Lipman–Zariski Conjecture in Low Genus

Published:2019-07-31 Issue:1 Volume:2021 Page:426-441
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Graf Patrick¹

Affiliation:

1. Lehrstuhl für Mathematik I, Universität Bayreuth, 95440 Bayreuth, Germany

Abstract

Abstract We prove the Lipman–Zariski conjecture for complex surface singularities of genus 1 and also for those of genus 2 whose link is not a rational homology sphere. As an application, we characterize complex $2$-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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/1/426/36348476/rnz154.pdf

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