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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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1 Answer 1

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

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  • $\begingroup$ Thank you very much! I think this definition is equivalent to the above one. $\endgroup$
    – MZWang
    Nov 22, 2010 at 11:20
  • $\begingroup$ Certainly it is since the sheafification functor is exact. $\endgroup$
    – Sasha
    Nov 22, 2010 at 11:53

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