Timeline for When is an algebraic variety $\mathbb{Q}$-factorial?
Current License: CC BY-SA 3.0
8 events
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| Aug 28, 2011 at 17:20 | history | edited | Donu Arapura | CC BY-SA 3.0 |
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| Aug 28, 2011 at 15:55 | vote | accept | Fei YE | ||
| Aug 28, 2011 at 15:19 | comment | added | Francesco Polizzi | @Ulrich: Right. In fact, it seems to me that the cone over $V \subset \mathbb{P}^n$ is normal if and only if $V$ is projectively normal | |
| Aug 28, 2011 at 15:08 | comment | added | naf | @Donu: It is not true that a cone over a smooth projective variety $V \subset \mathbb{P}^N$ is always normal. Hartshorne, AG, Ex I 3.18, given a twisted quartic curve in $\mathbb{P}^3$ as an example; the point here is that this is not a linearly normal embedding. | |
| Aug 28, 2011 at 14:12 | history | edited | Donu Arapura | CC BY-SA 3.0 |
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| Aug 28, 2011 at 14:07 | comment | added | Donu Arapura | No, I meant the opposite. Let me make a quick edit, in case it's unclear. | |
| Aug 28, 2011 at 13:42 | comment | added | Anton Geraschenko | Could you clarify the last (counter)example? If V is genus 0, a hyperplane section rationally generates. Are you claiming there is a higher genus curve V for which a hyperplane slice also generates? | |
| Aug 28, 2011 at 13:20 | history | answered | Donu Arapura | CC BY-SA 3.0 |