Timeline for Picard group of hypersurfaces in $\mathbb{P}^r\times\mathbb{P}^s$
Current License: CC BY-SA 4.0
18 events
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| Jan 19, 2021 at 23:00 | vote | accept | CommunityBot | ||
| Oct 7, 2020 at 13:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 9, 2020 at 12:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 10, 2020 at 11:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 11, 2020 at 10:38 | answer | added | user39380 | timeline score: 0 | |
| Jan 11, 2020 at 2:04 | history | edited | user39380 | CC BY-SA 4.0 |
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| Jan 11, 2020 at 1:57 | comment | added | user39380 | @Sasha It would be great if there’s result for any irreducible hypersurface, thanks! | |
| Jan 10, 2020 at 15:23 | comment | added | Sasha | I still don't understand --- you want the result for any hypersurface, or for some hypersurfaces? Perhaps, it makes sense to edit the question to make this clear. | |
| Jan 10, 2020 at 13:26 | history | edited | user39380 | CC BY-SA 4.0 |
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| Jan 10, 2020 at 13:15 | comment | added | user39380 | @Sasha Ah, sorry for my being imprecise.. If we consider the projection $\pi\colon\mathbb{P}^r\times\mathbb{P}^s\to\mathbb{P}^s$, then the restriction to $V(f)\to\mathbb{P}^s$ is a fibration in hypersurfaces. If we apply the Leray spectral sequence for the map, we want to delete a codimension 2 subvariety in $Z\subset V(f)$, so that $V(f)-Z\to\mathbb{P}^s-\pi(Z)$ is a fibration in constant Picard number 1. Thanks! | |
| Jan 10, 2020 at 12:53 | comment | added | Sasha | Codimension in the space of parameters? And I guess you mean Picard number greater than 2, right? | |
| Jan 10, 2020 at 12:48 | history | edited | user39380 | CC BY-SA 4.0 |
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| Jan 10, 2020 at 12:44 | comment | added | user39380 | @Sasha Yes, I am working on some problem which really needs the case for possibly singular hypersurfaces, thanks! By the Leray spectral sequence, it would be ok if codimension of locus whose Picard number greater than 1 has codimension at least two. | |
| Jan 10, 2020 at 12:33 | comment | added | Sasha | A general hyperusrface of bidegree $(d,1)$ smooth. Are you really interested in singular (non-general) hypersurfaces? | |
| Jan 10, 2020 at 12:21 | history | edited | user39380 | CC BY-SA 4.0 |
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| Jan 10, 2020 at 12:11 | history | edited | user39380 | CC BY-SA 4.0 |
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| Jan 10, 2020 at 9:34 | history | edited | user39380 | CC BY-SA 4.0 |
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| Jan 10, 2020 at 8:51 | history | asked | user39380 | CC BY-SA 4.0 |