The Lipman–Zariski Conjecture in Low Genus
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 bundl...
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Veröffentlicht in: | International mathematics research notices 2021-01, Vol.2021 (1), p.426-441 |
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Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | 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. |
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ISSN: | 1073-7928 1687-0247 |
DOI: | 10.1093/imrn/rnz154 |