In the following question (Direct Image by a Blow up) I have a question about the notation being used.
In this question, it is shown that $$\pi_{*}(\mathcal{O}_{\widetilde{X}}(-nE))= I_{Y/X}^{n}$$
where $\pi : \widetilde{X} \longrightarrow X$ is the blowing up of $X$ along a smooth subvariety $Y \subset X$ with exceptional divisor $E$.
Does the $I^{n}$ notation signify $\underbrace{I \otimes I \otimes \cdots \otimes I}_{n\ \textrm{times}}$ ?
Thank you very much.
No, it means the product of ideal sheaves, $I\cdot I \cdot \ldots \cdot I$. This is not in general the same as the version with tensor products.