Timeline for Principal Bundles over Complex Projective Varieties
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2010 at 16:00 | answer | added | Ben Webster♦ | timeline score: 2 | |
| Feb 6, 2010 at 15:14 | history | edited | Jean Delinez | CC BY-SA 2.5 |
edited title
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| Feb 6, 2010 at 15:06 | history | edited | Jean Delinez | CC BY-SA 2.5 |
added 442 characters in body; added 3 characters in body
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| Feb 6, 2010 at 13:49 | answer | added | Pavel Etingof | timeline score: 5 | |
| Feb 6, 2010 at 12:24 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
title fix + retag
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| Feb 6, 2010 at 10:12 | comment | added | José Figueroa-O'Farrill | I am not sure I understand this question. What in the principal fibration is supposed to be the complex projective variety? The base? The total space? In the examples you have provided, it seems that it is the base of the fibration. If so, then just simply take your favourite variety and stick a principal bundle on it. Clearly this is too trivial an answer, so more likely than not I'm misunderstanding the question. | |
| Feb 6, 2010 at 8:38 | comment | added | Jean Delinez | But isn't every homogeneous space automatically a principal bundle? As far as I can see, for any homogeneous $G$-space $X$, with stabilizer subgroup $H$ of some point $x \in X$, we have $X = G/H$. The projection $\pi:G \to G/H$, gives $G$ a fibred structure and the action of $H$ on the fibres is free and transitive, making $\pi:G \to X$ a principal $H$-bundle. Yes, all the examples I mentioned are homogeneous spaces, but I would be interested in examples that only principal bundles. | |
| Feb 6, 2010 at 6:32 | comment | added | Anton Geraschenko | It looks like you mean "homogeneous space" (space with a transitive group action) rather than "principal bundle" (morphism with a free transitive group action on fibers). | |
| Feb 6, 2010 at 6:18 | history | asked | Jean Delinez | CC BY-SA 2.5 |