Timeline for What do you call $x$ such that $\textrm{dim} f^{-1}(f(x))>0$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 4, 2023 at 1:44 | comment | added | H A Helfgott | @JasonStarr OK - it's all fine for my purposes. But can one also speak of the exceptional locus of $f'$ when $r>0$? | |
| Mar 4, 2023 at 1:05 | comment | added | Jason Starr | You are right. I misunderstood the question. You are looking at the inverse image of the image under $f$ of the exceptional locus of $f'$. | |
| Mar 3, 2023 at 10:22 | comment | added | H A Helfgott | Does one also capture the case $r>0$ in exactly the same way using the Stein factorization? | |
| Mar 2, 2023 at 15:14 | comment | added | H A Helfgott | What one gets then is not all $x$ such that $\textrm{dim} f^{-1}(f(x))>0$, but only those sitting in components of $f^{-1}(f(x))$ of positive dimension, right? | |
| Mar 2, 2023 at 13:49 | comment | added | Jason Starr | In that notation, the morphism $f’$ is birational, and your locus is the exceptional locus of this birational morphism. | |
| Mar 2, 2023 at 13:23 | comment | added | H A Helfgott | @JasonStarr : meaning what exactly, in the notation in en.wikipedia.org/wiki/Stein_factorization ? | |
| Mar 2, 2023 at 11:56 | comment | added | Jason Starr | It is the exceptional locus of the connected part of the Stein factorization. | |
| Mar 2, 2023 at 11:50 | history | asked | H A Helfgott | CC BY-SA 4.0 |