Timeline for Isotrivial Monodromy
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2018 at 17:28 | vote | accept | François | ||
| Aug 28, 2018 at 22:08 | comment | added | Jonny Evans | Ah ha, if your fibres are compact then there is a theorem of Grauert and Fischer tells you that your family is a locally trivial bundle (which I guess in my head is what I was assuming isotrivial meant, despite what I wrote). As your question was about projective families, this should be enough. Indeed, an easier way to say what I said would be: pick local trivialisations and your monodromy ends up being a composition of biholomorphic transition maps, hence it's biholomorphic. | |
| Aug 28, 2018 at 21:57 | comment | added | Jonny Evans | Possibly I'm missing some assumption about the existence of a suitable fine moduli space? I'll have a think. | |
| Aug 28, 2018 at 18:17 | comment | added | François | Thanks for your answer, Jonny Evans! I'm a little concerned that there is a detail missing because the second paragraph doesn't use compactness of the fibers at all. There are non-trivial holomorphic families of $\mathbb C^2$'s over a contractible base, for example. | |
| Aug 21, 2018 at 7:30 | history | answered | Jonny Evans | CC BY-SA 4.0 |