Timeline for Generic Smoothness Type of Results in Positive Characteristic
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2016 at 19:20 | comment | added | Jason Starr | Actually, as updated below, there are examples where the geometric generic fiber of $f$ is everywhere nonreduced. | |
| Feb 12, 2016 at 15:06 | vote | accept | Omprokash Das | ||
| Feb 12, 2016 at 13:40 | answer | added | Jason Starr | timeline score: 7 | |
| Feb 12, 2016 at 10:51 | comment | added | Jason Starr | Also, because the geometric generic fiber is $S2$, this is really about the codimension $1$ part of the singular locus of the morphism. So, via Bertini, etc., you may as well assume that $X$ is a surface and $Y$ is a curve. | |
| Feb 12, 2016 at 10:11 | comment | added | Jason Starr | If $X$ is smooth, then over a dense Zariski open subset of $Y$ the geometric fibers are LCI, hence Cohen-Macaulay. Also, if the natural map $\mathcal{O}_Y\to f_*\mathcal{O}_X$ is generically an isomorphism, then the geometric generic fiber is generically reduced. Hence the geometric generic fiber is (everywhere) reduced. | |
| Feb 12, 2016 at 6:23 | history | asked | Omprokash Das | CC BY-SA 3.0 |