Timeline for Elementary short exact sequence of sheaves
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| May 11, 2011 at 12:11 | comment | added | Jesus Martinez Garcia | You are absolutely right, thank you very much for your answer | |
| Apr 27, 2011 at 10:09 | comment | added | Francesco Polizzi | a) Well, $-3 < -2$, right? :-) b) You can contract any smooth rational curve with negative self-intersection (by Artin contractibility criterion), but in general the resulting surface is singular, unless you are contracting a $(-1)$-curve. c) Look at BPHV (Barth-Peters-Hulek-Van de Ven - the new edition) p. 99-105 | |
| Apr 27, 2011 at 9:58 | comment | added | Jesus Martinez Garcia | Thanks, this is quite interesting. However: a) you say before that the irreducible components of the minimal resolution will have self-intersection $\leq -2$, but in the case of $\mu_3$ they have -3. Why is this? b) According to Castelnuovo-Enriques contractibility criterion, when you blow-up or blow-down, the only divisor involved is a -1 line. I follow Beauville book. I suspect this because it only works on complex smooth surfaces c) I like the continues fraction bit. I fail to find it in BPV, though. Do you know a source which talks about this? | |
| Apr 27, 2011 at 7:39 | history | undeleted | Francesco Polizzi | ||
| Apr 27, 2011 at 7:38 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
added 321 characters in body; deleted 14 characters in body; deleted 19 characters in body
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| Apr 27, 2011 at 7:23 | history | deleted | Francesco Polizzi | ||
| Apr 27, 2011 at 7:22 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |