Timeline for Picard group of Fano varieties
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2023 at 11:48 | comment | added | Jason Starr | Yes, that is the paper. The result that I mean is Corollary 2.4: if the scheme deforms to characteristic $0$, and if $p$ is prime to the "torsion order" and the "uniruling index", then the Picard group is torsion-free. | |
| Feb 24, 2023 at 9:45 | comment | added | Daniel Loughran | @JasonStarr: Is this the paper "Weak approximation for Fano complete intersections in positive characteristic"? Where is the result in there? Also what is your intuition? Do you expect the Picard group to be always torsion-free? | |
| Feb 24, 2023 at 9:27 | comment | added | Daniel Loughran | @R.vanDobbendeBruyn: Just the smooth projective ones. It would be interesting to know however about related results or counter-examples for rationally (chain) connected varieties. | |
| Feb 24, 2023 at 0:30 | comment | added | Jason Starr | In my paper with Zhiyu Tian and Ruhong Zong, we also have some results if the Fano variety lifts to characteristic $0$. It seems like the hardest case is Fano varieties that do not lift to characteristic $0$. | |
| Feb 23, 2023 at 22:39 | comment | added | R. van Dobben de Bruyn | Are you primarily interested in smooth projective Fano varieties, or a more general notion? | |
| Feb 23, 2023 at 21:34 | history | asked | Daniel Loughran | CC BY-SA 4.0 |