Timeline for Principal bundle: A criterion
Current License: CC BY-SA 3.0
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Mar 26, 2017 at 3:56 | comment | added | Mee Seong Im | Since the $G$-action on $X$ is free, the quotient $X/G$ is a complex manifold [see Complex Tori and Abelian Varieties, by Olivier Debarre, page 75]. Since the $G$-action preserves the fibers of $X/G$, $X\rightarrow X/G$ is a principal $G$-bundle. | |
| Mar 26, 2017 at 2:39 | comment | added | nfdc23 | If you prefer French (resp. English) see Prop. 10, section 1.5, Chapter III of Bourbaki's Groupes et Alg`ebres de Lie (resp. Lie groups and Lie algebras) for such an action by any real or complex Lie group; also see Prop. 13 there. Also see section 12 in Chapter III of Part II of Serre's book "Lie groups and Lie algebras" (Springer LNM 1500) for a wider context (also treated elsewhere in Bourbaki). | |
| Mar 26, 2017 at 2:12 | history | asked | HLC | CC BY-SA 3.0 |