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Timeline for What are meromorphic line bundles?

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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
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
Mar 16, 2023 at 9:14 history asked მამუკა ჯიბლაძე CC BY-SA 4.0