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Ok, I have an affine (normal) toric variety $X = \text{Spec} k[\sigma]$. Suppose that $F, G$ are two torus invariant Weil divisors on $X$. Is there any relatively straightforward way to compute $$ \text{Ext}^i_{\mathcal{O}_X}(\mathcal{O}_X(F), \mathcal{O}_X(G))? $$ If it helps, I'm happy to assume that $F$ and $G$ are effective (one can twist to that case up to isomorphism anyways), but obviously I can't assume that $F$ is Cartier...

I'd be particularly interested in doing this if $X$ is dimension 3. Even (and perhaps especially for) specific examples.

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    $\begingroup$ I don't know the answer (or I would post it). However, I thought I'd mention that, last Spring, I was talking with David Treumann and Eric Zaslow about some toric questions, and they had some sort of mirror symmetry based intuition for computations like this. You might shoot them an e-mail. $\endgroup$ Aug 17, 2011 at 20:18
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    $\begingroup$ @Karl, just between us, you want $Ext^i(R/I, R/J)$ or $Ext^i(I,J)$? $\endgroup$ Aug 18, 2011 at 0:19
  • $\begingroup$ Hailong, it should translate to the second. $\endgroup$ Aug 18, 2011 at 0:32
  • $\begingroup$ I want the second. $\endgroup$ Aug 18, 2011 at 2:49

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