All Questions
Tagged with curves moduli-spaces
5 questions
6
votes
1
answer
766
views
Rationality of the moduli space of genus g curves
I'm not an expert in this topic, so please excuse my negligence. I'd also appreciate references to the literature. Throughout, I will work over the complex numbers, although the analogous questions ...
- 5,760
1
vote
0
answers
52
views
Understanding the Exp map from a moduli of smooth curves
The setup:
Suppose I'm given a family of class $C^k$ curves $\{f_{z}\}_{z\in Z}$ with values in $\mathbb{R}$ parameter by a finite number of parameters $Z\subseteq \mathbb{R}^m$.
Let $\mathscr{M}$ be ...
- 5,405
15
votes
1
answer
1k
views
Number of curves over a finite field
Let $K$ be a finite field. Is there a formula for the number of isomorphism classes of genus $g$ smooth curves over $K$?
In other words does there exists a formula for the number of rational points ...
- 8,998
2
votes
1
answer
669
views
Kodaira dimension of the moduli space of curves
It is known that the moduli space $\overline{M}_{g}$ of genus $g$ curves is of general type for $g\geq 24$.
By Theorem 2.4 of
Logan, Adam The Kodaira dimension of moduli spaces of curves with ...
- 8,998
16
votes
4
answers
3k
views
Moduli space of genus 2 curves
Does any body know any reference in which the geometry of compactified moduli space of genus two curves ( Which is a three dimensional variety/stack/...) has been studied?
