Timeline for Singularities of fibrations
Current License: CC BY-SA 3.0
4 events
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| Apr 16, 2017 at 1:26 | comment | added | Sándor Kovács | OK, so your fibers are not exactly as you originally described, but having reduced components in the fibers is not unusual. For instance, if you resolve the indeterminacy of the map $(x,y)\mapsto {y^2}/x$, you get exactly that behavior. | |
| Apr 15, 2017 at 17:24 | comment | added | Puzzled | Thanks a lot for the answer. In my case $X$ is a complete intersection $3$-fold in $\mathbb{P}^2\times\mathbb{P}^2\times\mathbb{P}^2$. So $X$ is Gorenstein. I checked that all the fibers of $f$ have dimension $1$ so from what you said $f:X\rightarrow \mathbb{P}^2$ is flat. But I just found a reducible fiber with a non reduced component (of multiplicity 2). How can this happen? In this situation shouldn't all the fibers be reduced? | |
| Apr 15, 2017 at 17:19 | vote | accept | Puzzled | ||
| Apr 15, 2017 at 2:36 | history | answered | Sándor Kovács | CC BY-SA 3.0 |