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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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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. –  David Speyer Aug 17 '11 at 20:18
    
@David, thanks, I'll ask them. –  Karl Schwede Aug 17 '11 at 22:16
    
@Karl, just between us, you want $Ext^i(R/I, R/J)$ or $Ext^i(I,J)$? –  Hailong Dao Aug 18 '11 at 0:19
    
Hailong, it should translate to the second. –  Donu Arapura Aug 18 '11 at 0:32
    
I want the second. –  Karl Schwede Aug 18 '11 at 2:49

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