The Lipman–Zariski Conjecture in Low Genus
| Autor: | Patrick Graf |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Tangent bundle Pure mathematics Conjecture Mathematics - Complex Variables General Mathematics Mathematics - Commutative Algebra Commutative Algebra (math.AC) Homology sphere Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Genus (mathematics) FOS: Mathematics Sheaf Complex Variables (math.CV) Locus (mathematics) Link (knot theory) Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | International Mathematics Research Notices. 2021:426-441 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnz154 |
| Popis: | 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 $2$-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. Comment: Published version is slightly shortened |
| Databáze: | OpenAIRE |
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