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....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2020-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509420000195/type/journal_article |
| _version_ | 1811156171335139328 |
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| author | HANNAH BERGNER PATRICK GRAF |
| author_facet | HANNAH BERGNER PATRICK GRAF |
| author_sort | HANNAH BERGNER |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T04:47:04Z |
| format | Article |
| id | doaj.art-4d619ffbae944f2caf9f32bc763c94c0 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:04Z |
| publishDate | 2020-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-4d619ffbae944f2caf9f32bc763c94c02023-03-09T12:34:48ZengCambridge University PressForum of Mathematics, Sigma2050-50942020-01-01810.1017/fms.2020.19THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHERHANNAH BERGNER0PATRICK GRAF1Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Ernst-Zermelo-Straße 1, 79104Freiburg im Breisgau, Germany;Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT84112, USA;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.https://www.cambridge.org/core/product/identifier/S2050509420000195/type/journal_article14B0514J1732S2513N15 |
| spellingShingle | HANNAH BERGNER PATRICK GRAF THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHER Forum of Mathematics, Sigma 14B05 14J17 32S25 13N15 |
| title | THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHER |
| title_full | THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHER |
| title_fullStr | THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHER |
| title_full_unstemmed | THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHER |
| title_short | THE LIPMAN–ZARISKI CONJECTURE IN GENUS ONE HIGHER |
| title_sort | lipman zariski conjecture in genus one higher |
| topic | 14B05 14J17 32S25 13N15 |
| url | https://www.cambridge.org/core/product/identifier/S2050509420000195/type/journal_article |
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