Timeline for Computing Picard groups of arbitrary quadric hyperplane
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 9, 2023 at 17:15 | review | Close votes | |||
| May 17, 2023 at 3:09 | |||||
| May 9, 2023 at 16:18 | history | edited | JKDASF | CC BY-SA 4.0 |
added 2 characters in body
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| Apr 18, 2023 at 19:18 | comment | added | roy smith | The nice comment of Jason, (project the quadric from a point of itself down one dimension), also explains why the theorem fails precisely for surfaces: smooth quadrics are reducible precisely in dimension zero! | |
| Apr 18, 2023 at 11:12 | comment | added | Jason Starr | This also follows by very simple methods as well: the blowing up of a smooth quadric at a point equals the blowing up of projective space along a smooth quadric whose dimension is two less. | |
| Apr 18, 2023 at 10:32 | comment | added | Daniel Loughran | .... this usually goes by the name "Lefschetz hyperplane section theorem". You can read about it in the book Lazarsfeld - Positivity in Algebraic Geometry I. | |
| Apr 18, 2023 at 2:12 | comment | added | Mohan | Smooth hypersurfaces in projective spaces $\mathbb{P}^n$ with $n\geq 4$ has Picard group $\mathbb{Z}$ generated by the hyperplane section. | |
| Apr 18, 2023 at 1:30 | history | asked | JKDASF | CC BY-SA 4.0 |