Timeline for Basepoints in the canonical system of algebraic surfaces
Current License: CC BY-SA 4.0
11 events
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| Sep 19, 2022 at 17:27 | history | edited | Sándor Kovács | CC BY-SA 4.0 |
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| Jan 14, 2013 at 3:22 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Nov 18, 2010 at 4:14 | vote | accept | Clay Cordova | ||
| Nov 17, 2010 at 16:21 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Nov 16, 2010 at 16:25 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Nov 16, 2010 at 15:54 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Nov 16, 2010 at 15:46 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Nov 16, 2010 at 15:35 | comment | added | Sándor Kovács | Francesco, you are absolutely right. I don't know what I was thinking... | |
| Nov 16, 2010 at 15:34 | history | edited | Sándor Kovács | CC BY-SA 2.5 |
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| Nov 16, 2010 at 10:09 | comment | added | Francesco Polizzi | Bombieri's theorem states that, for $n \geq 5$, the $n$-th pluricanonical map $S \to \mathbb{P}^N$ is a birational morphism onto its image, which contracts only the $(-2)$-curves of $S$. In particular it is everywhere defined and $|nK_X|$ is base-point free (moreover the image is isomorphic to the canonical model of $S$). Furthermore, $nK_S$ is spanned by global sections for $n \geq 4$. The main technical tool required is Ramanujam's vanishing theorem, which is not available in higher dimensions, so a straightforward generalization is not possible. | |
| Nov 16, 2010 at 8:45 | history | answered | Sándor Kovács | CC BY-SA 2.5 |