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Hello everyone,

A quick question, as I'm not sure I got it right.

Let $X=\mathbb{P}^1 \times \mathbb{P}^1$ and let $\mathcal{O}(a,b):=\pi^*_1\mathcal{O}(a)\otimes \pi^*_2\mathcal{O}(b)$. Is there a general expression for $$RHom_X(\mathcal{O}(a,b),\mathcal{O}(x,y))$$

Thank you

Edit: Whoops, I actually meant derived Hom, but I think I got it now

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  • $\begingroup$ Are you looking for something different than $H^0(X, \mathcal{O}(x-a, y-b))$? $\endgroup$
    – Mike Skirvin
    Commented Jun 30, 2010 at 17:52

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