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Each book on algebraic geometry write I^2 when it deal with nongsingular varieties, here I is a ideal sheaf. But no one give the definition. I guess it's the sheafification. It's right?

Thanks.

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up vote 2 down vote accepted

It is the image of the map $I \otimes I \to O \otimes O = O$.

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Thank you very much! I think this definition is equivalent to the above one. – MZWang Nov 22 '10 at 11:20
    
Certainly it is since the sheafification functor is exact. – Sasha Nov 22 '10 at 11:53

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