Timeline for $f^{-1}\mathcal I \cdot \mathcal O_X$ vs $f^\ast \mathcal I$
Current License: CC BY-SA 3.0
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| May 23, 2013 at 12:41 | comment | added | Sasha | A birational morphism is flat only if it is an open embedding. So, I doubt very much that the morphism you are interested in is flat. But of course, the flatness of the morphism is much stronger than what you want. For example, if $f$ is flat only over $Z$ everything is OK. | |
| May 23, 2013 at 10:24 | comment | added | user34290 | Thank you! I don't think this answer the question about the book of Faltings and Chai, since the morphism from the toroidal to the minimal compactification doesn't seem to be flat. Am I correct? | |
| May 23, 2013 at 9:43 | history | answered | Sasha | CC BY-SA 3.0 |