Let $S$ be an algebraic surface and $P,Q$ two points on it. Let $I_P$ and $I_Q$ denote the ideal sheaves of $P$ and $Q$ respectively. Which is the tor group $Tor^1(I_P,I_Q)$? And what about $Tor^1(I_P,I_P)$?
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$\begingroup$ Can you see what they are in the affine case? $\endgroup$– Mariano Suárez-ÁlvarezCommented Nov 2, 2010 at 14:31
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$\begingroup$ It seems to me that in the affine case $Tor^1(I_P,I_Q)=0$ if $P\neq Q$. $\endgroup$– ginevra86Commented Nov 2, 2010 at 15:24
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