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

Let $M_3$ be the moduli space of genus three curves over $\mathbb C$. Are there non-constant regular functions of this space? What about complex analytic functions?

This question is prompted by the following one : Does the moduli space of genus three curves contain a complete genus two curve

share|cite|improve this question
up vote 2 down vote accepted

Here's an older MO post addressing this question (which appears to apply to M_3, though I don't have Harris-Morrison handy): What is the affinization of M_g?

share|cite|improve this answer
Thanks a lot! Harris Morrison says indeed that if you take Satake compaction $\tilde M_g$ of $M_g$ then first of all it is projective and second $\tilde M_g\setminus M_g$ has codimension $2$ provided $g\ge 3$ (a bit surpising :)) . So there are plenty of curves on $\tilde M_g$ that miss $\tilde M_g\setminus M_g$. – aglearner Nov 6 '12 at 14:38

Your Answer


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.