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I know the title sounds too much general. Googling the question I have not found much material, so I decided to ask to experts. I would like to know which are the most famous/important unsolved conjectures for vector bundles on algebraic curves, which are the known consequences and why they seem evident.

Thank you

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closed as not a real question by Martin Brandenburg, Theo Johnson-Freyd, Dmitri Pavlov, Andreas Blass, Mariano Suárez-Alvarez Jun 30 '11 at 17:27

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

I had initially read your title as «Victor Bundles' conjectures» and I marveled at the guy ending up working on vector bundles... – Mariano Suárez-Alvarez Jun 30 '11 at 14:54
Hi unkn21: I think that this question is too open-ended for this forum, and so I've voted to close. I do recommend that you ask specific questions about your research re:vector bundles on algebraic curves. Also, please look over and read some of the successful MO questions for a sense of what types of questions work best here. In the meantime, it looks like you do have a correct answer below, from an unknown (google) account. – Theo Johnson-Freyd Jun 30 '11 at 16:28

There's an article "A problem list on vector bundles" written by Eduardo Ballico.You can find it in the book"Complex analysis and geometry" Edited by Vincenzo Ancona and Alessandro Silva,Plenum Press.I happen to know this article when reading another topic in this book.Maybe it is useful.

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