Timeline for What are meromorphic line bundles?
Current License: CC BY-SA 4.0
12 events
when toggle format | what | by | license | comment | |
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Mar 21, 2023 at 13:16 | answer | added | Misha Verbitsky | timeline score: 5 | |
Mar 17, 2023 at 8:51 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
explanations reacting to Eremenko's comment
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Mar 16, 2023 at 15:29 | comment | added | მამუკა ჯიბლაძე | @AlexandreEremenko Thank you, I am obviously too superficial. I do not even understand now what I should say about higher dimensional $V$. Probably for $V$ of dimension $n$ I should talk about maps to $\mathbb A^n$ vs maps to $\mathbb P^n$? Don't know... | |
Mar 16, 2023 at 14:01 | comment | added | Alexandre Eremenko | "Given, say, a regular function on V∖{a point} this function might have a pole of some order at that point, or an essential singularity" - are you talking about 1-dimensional $V$? In higher dimension a function regular on $V$ minus {point} cannot have a pole. | |
Mar 16, 2023 at 13:36 | comment | added | მამუკა ჯიბლაძე | @KevinCasto The only sensible thing I see is to use line bundles as some kind of transition functions - this is essentially what Brylinski does in the book I mention in that answer I linked to... | |
Mar 16, 2023 at 12:27 | review | Suggested edits | |||
Mar 16, 2023 at 13:21 | |||||
Mar 16, 2023 at 11:33 | comment | added | მამუკა ჯიბლაძე | You mean sheaf of functions to $\mathbb P^1$? But it does not have any group structure, does it? | |
Mar 16, 2023 at 11:14 | comment | added | Kevin Casto | Sure, they'll just be $H^1$ of $V$ with coefficients in the sheaf of transition functions I described, but that's kind of tautological. | |
Mar 16, 2023 at 11:07 | comment | added | მამუკა ჯიბლაძე | @KevinCasto Thank you, this sounds promising. Can the ones you mention be described by some kind of cohomology group? Do they have algebraic duals, analogous to fractional ideals or rank 1 projective modules? | |
Mar 16, 2023 at 10:34 | comment | added | Kevin Casto | You can certainly define a meromorphic line bundle as one where the transition functions can have zeros or poles along the divisor. Not sure what the classifying space for these would be in the sense you ask for | |
Mar 16, 2023 at 9:21 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
changed notation
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Mar 16, 2023 at 9:14 | history | asked | მამუკა ჯიბლაძე | CC BY-SA 4.0 |