Timeline for Picard of the product of two curves
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 20, 2014 at 21:22 | comment | added | Daniel Litt | It seems that it might be a bit easier to keep track of things if one uses the Leray spectral sequence for the maps $X\times Y\to X\to *$. Then one gets an exact sequence $$0\to \text{Pic}(X)\to \text{Pic}(X\times Y)\to H^0(X, \text{Pic}(Y))\to \text{Br}(X)$$ and we may write $H^0(X, \text{Pic}(Y))$ as $\text{Hom}(\text{Pic}^1(X), \text{Pic}(Y))$. I haven't thought very hard about when the last map in this sequence is zero, though... | |
| Nov 18, 2014 at 17:58 | comment | added | Sofia Tirabassi | Thank you very much for taking the time to explain everything to me. You are correct, of course, about the hypothesis. I apologize for the sloppiness. In truth I was just looking for a reference... this is so much better. Thank you very much! | |
| Nov 18, 2014 at 17:55 | vote | accept | Sofia Tirabassi | ||
| S Nov 18, 2014 at 5:46 | history | answered | user27920 | CC BY-SA 3.0 | |
| S Nov 18, 2014 at 5:46 | history | made wiki | Post Made Community Wiki by user27920 |