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Mar 7, 2014 at 1:38 comment added HNuer It follows from Grothendieck's vanishing theorem. that Ext group is the same thing as $H^{\dim X-i}(L^{-N}\otimes E(K_X))^*$, and this sheaf has support of dimension $\dim supp(E)$. If $\dim X-i>\dim supp(E)$, then this must vanish by Grothendieck's vanishing theorem.
Mar 6, 2014 at 7:54 comment added user133030 Why is the "this is zero for i<dimX−dimsupp(E)" in the 2nd sentence true?
Mar 6, 2014 at 7:34 history answered Sasha CC BY-SA 3.0