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

Does anyone know any information on the question of the dimension of moduli space of pointed curves with fixed Weierstrass semigroup? Some conjecture?

share|improve this question
1  
For those who (like me) didn't know the terminology: "Given a curve X over a field k, an object classically studied is the Weierstrass semigroup of a k-rational point P of X. This semigroup consists of those nonnegative integers n such that there is a rational function on X with a pole of order n at P and no other poles." –  JSE Dec 7 '09 at 4:41

2 Answers 2

If the complement of the semigroup (the gaps) is $a_1,\ldots,a_g$, then the weight is $w=\sum (a_i-i)$. I think you expect codimension $w-1$ (for small $w>0$) for the space of curves of genus $g$ having the given semigroup. However, this cannot work for large $w$. Have a look at the papers of Steven Diaz.

share|improve this answer

One good reference is "Recent progress in the study of Weierstrass points" by Eisenbud and Harris in Geometry Today, Birkhauser, 1985.

share|improve this answer

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.