Timeline for How to compute $\mathcal{Ext}^{i}_{X}(\mathcal{O}_{Y_{1}},\mathcal{O}_{Y_{2}})$?
Current License: CC BY-SA 3.0
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| Feb 29, 2012 at 13:47 | answer | added | Tony Pantev | timeline score: 8 | |
| Feb 27, 2012 at 18:26 | comment | added | Piotr Achinger | See Hartshorne, proof of Theorem III 7.11 - there he computes ${\scr E}xt^r(\mathcal{O}_{Y_1}, \omega_X)$ by applying $Hom(-, \Omega_X)$ to the Koszul complex of $\mathcal{O}_{Y_1}$. The Koszul complex exists only locally, but then he shows that these local calculations glue together. I think you can apply the same argument to $\mathcal{O}_{Y_2}$ in place of $\omega_X$. | |
| Feb 27, 2012 at 17:26 | history | asked | A. Pascal | CC BY-SA 3.0 |