Timeline for Line bundles and vector bundles on $\mathbb P^1 \times \mathbb P^1$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 20, 2023 at 21:01 | comment | added | user505117 | @Sasha "There is a lot of literature on the subject." Can you give examples? I find nothing specific for $\mathbb{P}^1 \times \mathbb{P}^1$ except Huh: "Moduli of stable sheaves on a smooth quadric and a Brill–Noether locus" and Huh: "Cubic symmetroids and vector bundles on a quadric surface". I do find much work on complex surfaces that is not specific to $\mathbb{P}^1 \times \mathbb{P}^1$. | |
| Jan 28, 2013 at 18:41 | comment | added | Allen Knutson | Angelo was trying to link to mathoverflow.net/questions/21854/… | |
| Jan 28, 2013 at 8:34 | comment | added | Angelo | For some further references, see <mathoverflow.net/questions/21854/…>. | |
| Jan 28, 2013 at 8:14 | answer | added | Daniel Litt | timeline score: 8 | |
| Jan 28, 2013 at 7:06 | comment | added | Sasha | For each triple $(r,c_1,c_2)$ there is a moduli space of stable vector bundles, which is not well understood. There is a lot of literature on the subject. | |
| Jan 28, 2013 at 6:50 | comment | added | Will Sawin | 2 is true by the exponential exact sequence $ H^1(X,\mathcal O_X) \to H^1(X,\mathcal O_X^\times) \to H^2(X,\mathbb Z)$, plus a computation of $H^1(\mathbb P^1 \times \mathbb P^1,\mathcal O_X)$ and $H^2(\mathbb P^1 \times \mathbb P^1,\mathbb Z)$, via the Kunneth formula, from the well known-cohomology of $\mathbb P^1$. | |
| Jan 28, 2013 at 6:05 | history | asked | Paul Graaf | CC BY-SA 3.0 |