THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHER
We prove the Lipman–Zariski conjecture for complex surface singularities with $p_{g}-g-b\leqslant 2$. Here $p_{g}$ is the geometric genus, $g$ is the sum of the genera of exceptional curves and $b$ is the first Betti number of the dual graph. This improves on a previous result of the second author....
| Huvudupphovsmän: | , |
|---|---|
| Materialtyp: | Artikel |
| Språk: | English |
| Publicerad: |
Cambridge University Press
2020-01-01
|
| Serie: | Forum of Mathematics, Sigma |
| Ämnen: | |
| Länkar: | https://www.cambridge.org/core/product/identifier/S2050509420000195/type/journal_article |
| Sammanfattning: | We prove the Lipman–Zariski conjecture for complex surface singularities with $p_{g}-g-b\leqslant 2$. Here $p_{g}$ is the geometric genus, $g$ is the sum of the genera of exceptional curves and $b$ is the first Betti number of the dual graph. This improves on a previous result of the second author. As an application, we show that a compact complex surface with a locally free tangent sheaf is smooth as soon as it admits two generically linearly independent twisted vector fields and its canonical sheaf has at most two global sections. |
|---|---|
| ISSN: | 2050-5094 |