Timeline for Deformation of $\mathbb{P}^1 \times \mathbb{P}^1$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| May 22, 2016 at 18:25 | comment | added | Allen Knutson | (1) Let me change it to: smooth proper families $F \to S$ with nonisomorphic fibers. In the complex case, all the fibers will be diffeomorphic. (2) I'm pretty sure I'd only expect etale-locally trivial (again, with $\mathbb P^1$-fiber for simplicity) but I don't have an example off the top of my head. | |
| May 21, 2016 at 0:54 | comment | added | Li Yutong | Thank you very much for you explanation! I have two questions according to your answer: (1) Does "moduli space of complex varieties with a fixed underlying real manifold" make sense in general? (2) Is this rigidity the same as "there exists a $U$ such that $F_U \cong U \times (\mathbf{P}^1 \times \mathbf{P}^1)$"? Or weaker than this locally triviality? | |
| May 21, 2016 at 0:48 | vote | accept | Li Yutong | ||
| May 20, 2016 at 17:51 | history | answered | Allen Knutson | CC BY-SA 3.0 |