Timeline for glue together a sequence of holomorphic forms
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2011 at 22:26 | comment | added | Henri | Maybe you could do that if you allow the global form to have values in some vector bundle. In this case, you have to check if your local values satisfy the cocycle identity (more precisely, if $s_k$ are the local values, you must find some invertible (holomorphic) matrices $g_{kl}$ satisfying $s_k=g_{kl} s_l$ and also the cocycle identities) | |
| Aug 14, 2011 at 20:53 | comment | added | Samuele | Just to make an example, take $M=\mathbb{CP}^1=\mathbb{C}\cup\\{\infty\\}$. Take $U_1=\mathbb{C}$ and $U_2=\mathbb{C}^*\cup\\{\infty\\}$, $\alpha_1=e^{z}dz$, $\alpha_2=e^{1/z}dz$. How could you glue them? What conditions of "compatibility" would you like to ask for? I mean, what should the link between the data and the result be, apart from the latter being a holomorphic (or meromorphic) form? | |
| Aug 14, 2011 at 20:36 | comment | added | dimitry | how to modify them? can you give a short example? | |
| Aug 14, 2011 at 20:12 | comment | added | Donu Arapura | I'm not sure what "glue together" would mean then. You'd have to modify them first, but I'm not sure what you allow. | |
| Aug 14, 2011 at 19:51 | comment | added | dimitry | Yes but if they do not agree on the cuts, is there any possibility to glue them together? | |
| Aug 14, 2011 at 19:51 | comment | added | Andreas Blass | And in the contrary case, certainly no. | |
| Aug 14, 2011 at 19:46 | comment | added | Donu Arapura | Are you assuming that $\alpha_k$ and $\alpha_\ell$ agree on $U_k\cap U_\ell$? In this case, certainly yes. | |
| Aug 14, 2011 at 19:30 | history | asked | dimitry | CC BY-SA 3.0 |