Timeline for Moduli space of (all) vector bundles on $\mathbb{P}^1$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Apr 5, 2016 at 10:48 | answer | added | Johan | timeline score: 3 | |
| Apr 1, 2016 at 22:14 | answer | added | Alexander Braverman | timeline score: 9 | |
| Apr 1, 2016 at 18:48 | comment | added | Jason Starr | For any (split) reductive group $G$ with maximal torus $T$ and Weyl group $\mathcal{W}$, Grothendieck proves that the set of $G$-torsors over $\mathbb{P}^1$ is naturally in bijection with the quotient of the cocharacter lattice of $T$, $\text{Hom}_{\textbf{GpSch}_k}(\mathbb{G}_{m,k},T)/\mathcal{W}$, where the $\mathcal{W}$-action is the natural action on $T$. Up to choosing a Weyl chamber of the cocharacter lattice, the specialization order should be something like adding the positive coroots. | |
| Apr 1, 2016 at 18:33 | comment | added | Jason Starr | The theorem that you attribute to Grothendieck was first proved by Del Pezzo and Bertini (cf. the article of Harris on varieties of minimal degree). It was then rediscovered by Birkhoff. Grothendieck proved a vast generalization of this theorem. There is a beautiful article of Martens and Thaddeus on Grothendieck's theorem and its extensions. | |
| Apr 1, 2016 at 18:26 | history | asked | Qfwfq | CC BY-SA 3.0 |