Timeline for A key step in Del Busto's effective Matsusaka theorem
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 4, 2015 at 23:05 | vote | accept | lemiller | ||
| Jun 4, 2015 at 21:42 | comment | added | Hacon | OK. Happy that it seems to help. | |
| Jun 4, 2015 at 21:41 | answer | added | Hacon | timeline score: 1 | |
| Jun 4, 2015 at 21:31 | comment | added | lemiller | @Hacon also it seems your equation array has a markdown error. If you type your comment as an answer I can accept it. | |
| Jun 4, 2015 at 21:27 | comment | added | lemiller | @Hacon Thanks a bunch! That's exactly what I hoping to see. I think the induction when eta_i > 1 is what was tricky to see, but as you noted, you can still induce and so your argument I think works. Also, in case anyone else is interest, there is a subtle change of setting in del Busto's proof. In particular, he really shows that a different lower bound on k implies being (k+1)-jet ample, but his theorem stated on the bottom of page 4 changes everything (hypothesis and conclusion) back to the k-jet ample! | |
| Jun 4, 2015 at 21:19 | comment | added | Hacon | It seems to me that $[(1/n)F_n]$ is exc. and there is a ses inducing $W(k)\to V(k+1)\to H^1((-\sum k_iE_i)|_{\sum \eta _iE_i})$ which has positive degree on a bunch of (non-reduced $\mathbb P^1$'s and so vanishes. If each $\eta _i\in \{0,1\}$, this is clear, if not proceed by induction via the ses of the form $0\to (-k-(\eta-1))E)|_E\to (-kE)|_{\eta E)\to (-kE)|_{(\eta -1)E}\to 0$ (hopefully I got the algebra right) | |
| Jun 3, 2015 at 19:09 | history | edited | lemiller | CC BY-SA 3.0 |
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| Jun 2, 2015 at 18:58 | history | edited | lemiller | CC BY-SA 3.0 |
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| Jun 1, 2015 at 14:41 | history | asked | lemiller | CC BY-SA 3.0 |