Timeline for Non-uniruled connected smooth fibers implies flat
Current License: CC BY-SA 4.0
6 events
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| Aug 29, 2020 at 12:42 | comment | added | Jason Starr | "Can the general fiber be e.g. a point and the special fiber be an elliptic curve?" Welcome new contributor. That certainly cannot happen. Abyhankhar proved that for a birational morphism to a smooth target the irreducible components of fibers are point or ruled varieties. That suggests an approach to your general question. Consider the rational transformation from $Y$ to the Chow variety of $X$ determined by the fibers of $f$. If the morphism is not flat, then the closure of the graph of this rational transformation has some uniruled fibers . . . | |
| Aug 29, 2020 at 6:52 | comment | added | Nguyen | @AmorFati all fibers are smooth | |
| Aug 29, 2020 at 6:43 | comment | added | AmorFati | All fibers are smooth, or the generic fiber is smooth? | |
| Aug 29, 2020 at 6:13 | history | edited | Nguyen | CC BY-SA 4.0 |
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| Aug 28, 2020 at 15:55 | history | edited | Nguyen | CC BY-SA 4.0 |
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| Aug 28, 2020 at 11:18 | history | asked | Nguyen | CC BY-SA 4.0 |