Timeline for Degenerations of rationally connected varieties
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2022 at 14:11 | comment | added | Daniel Loughran | @FrancescoPolizzi: The picture to have in mind is a family of varieties over $\mathbb{P}^1$ whose generic fibre is rationally connected, then trying to find a birational modification of the family all of whose singular fibres contain no multiple components. | |
| Jul 26, 2022 at 13:15 | comment | added | Jason Starr | My intuition is that this is false, but I do not have a counterexample at hand. The result by Koll’ar in the case of a Fano fibration only gives a “canonical” irreducible component of multiplicity one (and over $\mathbb{C}$ that already follows from the work of Graber, Harris, Mazur and myself). The work of Hogadi-Xu is similar. | |
| Jul 26, 2022 at 12:50 | comment | added | Laurent Moret-Bailly | @FrancescoPolizzi I think $X$ is defined over $\mathbb{C}((t))$, not $\mathbb{C}$. | |
| Jul 26, 2022 at 11:44 | comment | added | Francesco Polizzi | But still I do not understand the question. There is always the trivial family $\mathcal{X}=X \times \operatorname{Spec}(R)$, right? Maybe you want some additional condition? | |
| Jul 26, 2022 at 11:11 | history | edited | Daniel Loughran | CC BY-SA 4.0 |
added 45 characters in body
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| Jul 26, 2022 at 11:10 | comment | added | Daniel Loughran | Yes, added thanks! | |
| Jul 26, 2022 at 11:06 | comment | added | Francesco Polizzi | You want the general fibre isomorphic to $X$, I presume. | |
| Jul 26, 2022 at 10:47 | history | asked | Daniel Loughran | CC BY-SA 4.0 |