Timeline for Equivalence between coactions and actions plus a linearization line bundle
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| S Apr 26, 2021 at 21:08 | history | suggested | tinlyx | CC BY-SA 4.0 |
improved formatting
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| Apr 26, 2021 at 18:25 | review | Suggested edits | |||
| S Apr 26, 2021 at 21:08 | |||||
| Nov 7, 2020 at 12:54 | comment | added | Mark Wildon | I’m voting to close this question because it appears to have been answered to the poster's satisfaction in a comment. | |
| Nov 5, 2020 at 6:30 | comment | added | Kim | @abx Now I got it. Thank you!! | |
| Nov 4, 2020 at 14:44 | comment | added | abx | Use the surjective homomorphism $V\otimes _{\mathbb{C}}\mathscr{O}_{\mathbb{P}}\rightarrow \mathscr{O}_{\mathbb{P}}(1)$. The natural $\operatorname{GL}(V) $-linearization of $V\otimes _{\mathbb{C}}\mathscr{O}_{\mathbb{P}}$ induces one on $\mathscr{O}_{\mathbb{P}}(1)$. | |
| Nov 4, 2020 at 14:02 | comment | added | Kim | @abx Can you give any more details about the "Conversely" part? Thanks! | |
| Nov 4, 2020 at 12:58 | comment | added | abx | For any line bundle $L$ on a variety $X$, a $G$-linearization induces a linear action of $G$ on $H^0(X,L)$. Conversely, a linear action of $G$ on $V$ induces an action on $\mathbb{P}(V)$ with a $G$-linearization of $\mathscr{O}_{\mathbb{P}}(1)$. | |
| Nov 4, 2020 at 9:23 | review | Suggested edits | |||
| Nov 4, 2020 at 19:34 | |||||
| Nov 4, 2020 at 9:02 | comment | added | Kim | @abx It seems that $H^0(\mathbb{P}(V), \mathcal{O}(1))=V$ in this book... I add the picture of the proof of Proposition 1.7 in question. | |
| Nov 4, 2020 at 9:01 | history | edited | Kim | CC BY-SA 4.0 |
added 81 characters in body
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| Nov 4, 2020 at 7:48 | review | Close votes | |||
| Nov 7, 2020 at 19:33 | |||||
| Nov 4, 2020 at 7:30 | comment | added | abx | Are you aware that $H^0(\mathbb{P}(V),\mathscr{O}_{\mathbb{P}}(1))=V^*$? That helps... | |
| Nov 4, 2020 at 2:04 | history | edited | Kim | CC BY-SA 4.0 |
added 68 characters in body
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| Nov 4, 2020 at 2:02 | comment | added | Kim | @abx Sorry, I mean the dual action. | |
| Nov 3, 2020 at 9:15 | comment | added | abx | What is a coaction? The term does not appear in Mumford's book. | |
| Nov 3, 2020 at 7:56 | review | First posts | |||
| Nov 3, 2020 at 8:32 | |||||
| Nov 3, 2020 at 7:48 | history | asked | Kim | CC BY-SA 4.0 |