Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I'm looking for a small research problem an undergraduate would be capable of after taking just an abstract algebra course, introductory algebraic geometry (at level of Miles Reid's book and Ideals, Varieties & Algorithms), and a course in number theory. Is there a website that would have a decent listing, or possibly a book one can recommend that may have small open research problems?

share|improve this question
8  
Open problems in algebraic geometry accessible to an advanced undergraduate seem scarce enough that I would keep any I thought of as trade secrets. And at this moment I can't think of anything else mathematical I would keep as a trade secret! –  Alexander Woo Jun 15 '10 at 17:03

1 Answer 1

up vote 2 down vote accepted

Your question is missing a crucial word in the first sentence (capable of ...). Is the missing word "understanding" or "solving"?

Anyway, here is a problem: Find the maximum number of points of a curve of genus $g$ over $\mathbb{F}_q$, for some values of $g,q$ for which this number is not known (check for values at http://www.manypoints.org/ )

share|improve this answer
    
@Felipe, I will be amazed if someone who knows algebraic geometry from the given sources can deal with it over a field not algebraically closed. Also, Reid's book avoids Riemann-Roch, so genus will be tough to use algebraically, let alone over finite fields. There's always plane curves, but undergraduate research in these areas seems a dubious idea. Perhaps another crucial word is missing: elementary number theory or algebraic number theory? –  Boyarsky Jun 15 '10 at 18:11

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.