Timeline for Deformations of a blowup
Current License: CC BY-SA 3.0
11 events
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| Feb 20, 2015 at 23:43 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Feb 20, 2015 at 21:54 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Feb 20, 2015 at 21:42 | comment | added | jmc | Thanks, I think that is clearer. (But now you also have $k_{s}$ in the long exact sequence, where it actually should be $k$, right?) Anyway, I do get your answer, and it very clear. Thanks for your effort! | |
| Feb 20, 2015 at 21:40 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Feb 20, 2015 at 21:38 | comment | added | Francesco Polizzi | I edited the answer writing $k_s \oplus k_s$ instead of $k \oplus k$. | |
| Feb 20, 2015 at 20:08 | vote | accept | jmc | ||
| Feb 20, 2015 at 20:08 | comment | added | jmc | Sorry for my ignorance. I confused the notation $k \oplus k$ with the constant sheaf; but I guess it was implicit that you meant the skyscraper sheaf. | |
| Feb 20, 2015 at 18:23 | comment | added | Francesco Polizzi | Right, it is a skyscraper sheaf supported on $s$. The exact sequence I wrote follows by applying $\beta_*$ to the exact sequence $$0 \to T_X \to \beta^* T_S \to \mathcal{O}_E(1) \to 0.$$ | |
| Feb 20, 2015 at 16:50 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Feb 20, 2015 at 16:47 | comment | added | jmc | Awesome, thanks! Seems I need to get hold of another book by Hartshorne (-; I don't get the short exact sequence though. The first two sheaves are isomorphic outside $s$, right? So the $k \oplus k$ should be a skyscraper supported on $s$, right? Or am I messing up in a stupid way? | |
| Feb 20, 2015 at 16:38 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |