Timeline for Uniformity of ampleness
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2010 at 15:04 | comment | added | diverietti | Ottem, would you prefer a complete proof in the general case? | |
| Dec 7, 2010 at 12:42 | comment | added | diverietti | On the other hand, of course the "global approach" two doesn't work in higher dimension, since the difference of two exceptional divisors coming form the blow-up of two different points is never zero in cohomology. But it was so simple, that I wanted to post it anyway. :) | |
| Dec 7, 2010 at 1:13 | comment | added | diverietti |
I mean, you have to arrange it a little bit, but nothing mysterious... Just use a tubular neighborhood of the exceptional divisor E on the blown-up manifold $\tilde X$ and extend the natural metric of $\mathcal O_E(−E)$ in an arbitrary way to a metric on $\mathcal_{\tilde X} O(-E)$.
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| Dec 7, 2010 at 1:02 | comment | added | diverietti | Not at all!! You can reproduce word-by-word the first argument just replacing the points with the exceptional divisors... | |
| Dec 7, 2010 at 1:00 | history | edited | diverietti | CC BY-SA 2.5 |
simplified the second argument.
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| Dec 7, 2010 at 0:56 | comment | added | J.C. Ottem | The curve case is perhaps a bit degenerate in this question. | |
| Dec 7, 2010 at 0:46 | history | answered | diverietti | CC BY-SA 2.5 |