Timeline for A deformation of the second Hirzeburch surface $F_2$ over $\mathbb CP^1$
Current License: CC BY-SA 4.0
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| Jun 17, 2019 at 21:55 | history | edited | aglearner | CC BY-SA 4.0 |
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| Jun 17, 2019 at 20:03 | comment | added | aglearner | That is an interesting conjecture | |
| Jun 17, 2019 at 13:52 | comment | added | Piotr Achinger | It seems reasonable to conjecture that they are all obtained from the one above by pullback along an endomorphism of P1 totally ramified at 0. | |
| Jun 17, 2019 at 11:20 | history | edited | aglearner | CC BY-SA 4.0 |
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| Jun 17, 2019 at 11:07 | comment | added | aglearner | Thanks for this comment! Indeed the first half of my question seems to be answered in the post you refer to. There is still a second part... What can be said in general about this type of three-folds? Is there a "simplest" among them? | |
| Jun 17, 2019 at 10:44 | comment | added | Piotr Achinger | Seems that your question is almost a duplicate of mathoverflow.net/questions/80989/… | |
| Jun 17, 2019 at 10:10 | comment | added | aglearner | Thanks Piotr. Could you point me to a nice reference for this standard degeneration, so that by reading it I would be able to fully understand your comment? | |
| Jun 17, 2019 at 10:08 | history | edited | aglearner | CC BY-SA 4.0 |
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| Jun 17, 2019 at 9:50 | comment | added | Piotr Achinger | Of course. Cover $\mathbf{P}^1$ by two copies of $\mathbf{A}^1$. Over one of those, construct the standard degeneration of $\mathbf{P}^1\times \mathbf{P}^1$ to $F_2$ (by degenerating the Euler sequence on $\mathbf{P}^1$ to a split sequence and taking the projective bundle). On the other copy, take the trivial family $\mathbf{P}^1\times \mathbf{P}^1 \times \mathbf{A}^1$. Identify the two families on the overlap. | |
| Jun 17, 2019 at 9:15 | history | asked | aglearner | CC BY-SA 4.0 |