Timeline for Rationality in pencil of projective varieties
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 4, 2021 at 2:22 | vote | accept | Ron | ||
| Jun 3, 2021 at 10:34 | comment | added | Puzzled | It is ok when $\mathcal{X}$ is a surface and $\pi$ has connected fibers. In this case you do not need the general fiber to be smooth, irreducible is enough. | |
| Jun 2, 2021 at 16:13 | comment | added | Jason Starr | According to a conjecture of Gino Fano, the total space of a sufficiently general conic bundle over a rational surface, say $\mathbb{P}^1\times\mathbb{P}^1$, is not unirational. This would give a counterexample to all three of your properties via projection to one of the two $\mathbb{P}^1$ factors. | |
| Jun 2, 2021 at 16:04 | answer | added | abx | timeline score: 7 | |
| Jun 2, 2021 at 14:28 | history | asked | Ron | CC BY-SA 4.0 |