Timeline for line bundle descends?
Current License: CC BY-SA 3.0
15 events
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| Jan 21, 2016 at 9:53 | comment | added | abx | I gave the precise condition in my answer, please read it. | |
| Jan 21, 2016 at 6:54 | comment | added | Karthik | Just a small clarification. An equivariant line bundle may not always descent to the quotient. Then what do you mean by there is a bijection between line bundles on the quotient and equivariant line bundles on the projective space ? The paper is in french, so I could not read the proof of theorem 2.3. | |
| Jan 19, 2016 at 11:22 | comment | added | abx | What's special about $\Bbb{P}^n$? The Drezet-Narasimhan paper gives everything in general. | |
| Jan 19, 2016 at 10:16 | comment | added | Karthik | Thank you for the clarification. Ok, its unique. Could you please give me a reference where the bijection is given for $\mathbb P^n$ ? | |
| Jan 18, 2016 at 15:29 | comment | added | abx | @Karthik: abelian subquotient = abelian quotient of a subgroup. And yes, there is a bijection between line bundles on the quotient and equivariant line bundles on $\Bbb{P}^3$. | |
| Jan 18, 2016 at 12:15 | comment | added | Karthik | @abx What do you mean by abelian subquotient here ? Again, is the descent unique ? | |
| Jan 28, 2015 at 13:06 | comment | added | abx | Yes, that's correct. | |
| Jan 28, 2015 at 9:47 | comment | added | Ram | I think the same proof will work for any $k$ a multiple of $2,3,...,n$ with the action of $S_n$ on $\mathbb P^{n-1}$. | |
| Jan 27, 2015 at 13:49 | comment | added | abx | Yes, of course, I meant an equivariant line bundle. A good reference is Theorem 2.3 in the paper of Drezet and Narasimhan, Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. math. 97 (1989), 53-94. | |
| Jan 27, 2015 at 13:37 | comment | added | Niels | The statement "By a result of Kempf a line bundle $L$ on $\mathbb{P}^3$ descends to the quotient if and only if the stabilizer $S_x$ of each point $x\in \mathbb{P}^3$ acts trivially on the fiber $L_x$." is not very precise. You probably mean : an equivariant line bundle, else the action on the fiber is not even defined. Could you give a reference ? | |
| S Jan 27, 2015 at 10:42 | history | edited | Marco Golla | CC BY-SA 3.0 |
O(1) tensor power 12 descends.
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| S Jan 27, 2015 at 10:42 | history | suggested | Ram | CC BY-SA 3.0 |
O(1) tensor power 12 descends.
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| Jan 27, 2015 at 10:40 | review | Suggested edits | |||
| S Jan 27, 2015 at 10:42 | |||||
| Jan 27, 2015 at 10:33 | vote | accept | Ram | ||
| Jan 27, 2015 at 10:30 | history | answered | abx | CC BY-SA 3.0 |