Timeline for Do smooth projective maps to $\mathbb{P}^1$ in positive characteristic have sections?
Current License: CC BY-SA 4.0
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| Nov 9, 2021 at 11:13 | comment | added | Jason Starr | I believe the symplectic proof of existence of holomorphic sections of a projective smooth morphism to $\mathbb{CP}^1$ also works if there is a single critical value. Glue the $2$-sphere to an "opposite" $2$-sphere along the boundaries of little disks centered at the critical values, and form the fibration over this new $2$-sphere by glueing the original fibration to its "opposite" fibration over the boundary of the disks. So one could ask about the positive characteristic case with a single critical value, but this fails since the fundamental group of $\mathbb{A}^1$ is nontrivial. | |
| Nov 7, 2021 at 18:10 | answer | added | Emiliano Ambrosi | timeline score: 1 | |
| Nov 7, 2021 at 17:33 | history | edited | Ben C | CC BY-SA 4.0 |
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| Nov 7, 2021 at 10:44 | history | asked | Ben C | CC BY-SA 4.0 |