Timeline for Invariance of Chow groups of projective bundles under automorphisms of bundles
Current License: CC BY-SA 4.0
17 events
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| Dec 8, 2020 at 19:12 | comment | added | Eoin | @abx ¸„.-•~¹°”ˆ˜¨ ~~!@@~!~✿✾~ＳỮ𝐫𝐫ᗴ𝐀Ĺ𝐢ⓈŦᶤ匚~~✴✽~!!~~^~ ¨˜ˆ”°¹~•-.„¸ | |
| Dec 7, 2020 at 15:51 | history | edited | Eoin | CC BY-SA 4.0 |
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| Dec 7, 2020 at 6:35 | comment | added | abx | This discussion is surrealistic. Have you seen Jason Starr's comment? | |
| Dec 7, 2020 at 4:04 | comment | added | Nanjun Yang | Maybe the invariance of $O(1)$ is trivial. It's something like given a sheaf $R$ of graded rings and a graded automorphism $f$ of $R$, prove that the two $R$-module structures of $R[1]$ are isomorphic. But the isomorphism is just given by $f[1]$! The same argument maybe false if we replace $R[1]$ by a graded module! | |
| Dec 7, 2020 at 2:04 | comment | added | Eoin | @NanjunYang I think that does it! | |
| Dec 7, 2020 at 2:04 | history | edited | Eoin | CC BY-SA 4.0 |
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| Dec 7, 2020 at 0:50 | vote | accept | Nanjun Yang | ||
| Dec 7, 2020 at 0:46 | comment | added | Nanjun Yang | Thanks. I think if $E=O_X^{\oplus n+1}$ is a trivial bundle, the $O(1)$ will be preserved. This is because the bundle $M$ you mentioned is the pullback of $O(1)$ along the composite $X\to X\times\mathbb{P}^n\to X\times\mathbb{P}^n\to\mathbb{P}^n$, which factors through $GL_{n+1}$. Then use $CH^1(GL_{n+1})=0$ to conclude that $M=O_X$. | |
| Dec 6, 2020 at 22:21 | history | undeleted | Eoin | ||
| Dec 6, 2020 at 22:21 | history | edited | Eoin | CC BY-SA 4.0 |
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| Dec 6, 2020 at 20:43 | history | edited | Eoin | CC BY-SA 4.0 |
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| Dec 6, 2020 at 17:21 | history | deleted | Eoin | via Vote | |
| Dec 6, 2020 at 16:41 | history | edited | Eoin | CC BY-SA 4.0 |
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| Dec 6, 2020 at 6:48 | comment | added | Nanjun Yang | How did you perform the last step to prove the middle arrow is the identity? | |
| Nov 8, 2020 at 21:53 | vote | accept | Nanjun Yang | ||
| Dec 6, 2020 at 6:47 | |||||
| Nov 8, 2020 at 18:10 | history | edited | Eoin | CC BY-SA 4.0 |
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| Nov 8, 2020 at 16:14 | history | answered | Eoin | CC BY-SA 4.0 |