MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Do you know calculate the dimension of the space of rational curves of degree m, through d given points, contained in some projective variety?

share|cite|improve this question
The question seems a bit broad, since there is a large body of work on this topic. Anyway, the short answer is "no": for instance, it is not even known in general how to prove that lines on a Fano hypersurface (through d=0 points) have the expected dimension. But you can look at papers of Beheshti, Landsberg, Starr and others to find positive results in this direction. (Hopefully the last-named author will be along presently to give you a more complete answer.) – user5117 Aug 19 '12 at 20:27
@Artie: I like your answer. – Jason Starr Aug 19 '12 at 21:18

Your Answer


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

Browse other questions tagged or ask your own question.