Timeline for group actions on blow-ups
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 15, 2022 at 9:46 | comment | added | H U | @Baobab The comment "the inverse image of $Z$ with respect to the morphism $G\times X\rightarrow X$ is $G\times X$" is needed to apply the universal property of blow ups. See Chapter 2, Prop 7.14 of Hartshorne. Also yes the final comment should be "gives an action of $G$ on $\tilde{X}$". | |
| Sep 30, 2020 at 15:38 | comment | added | Baobab | I apologize since the post is quite old, but I don't understand some passages: which do you need to say that the inverse image of $Z$ is $G\times Z$ (i.e., where do you use it?)? isn't there a typo on the sentence "the morphism $G\times \tilde{X}\to \tilde{X}$ gives an action of $G$ to $X$: shouldn't there be written an action to $G$ on $\tilde{X}$? Thanks in advance for the patience. | |
| Feb 26, 2013 at 23:53 | comment | added | Jérémy Blanc | It works in fact for any group. Not necessarily algebraic... | |
| Feb 26, 2013 at 9:05 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Feb 25, 2013 at 20:52 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
added 83 characters in body
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| Feb 25, 2013 at 20:46 | history | answered | Daniel Loughran | CC BY-SA 3.0 |