pith. sign in

arxiv: math/0611815 · v2 · submitted 2006-11-27 · 🧮 math.AG

Cohomology of moduli spaces of curves of genus three via point counts

classification 🧮 math.AG
keywords curvesgenusmodulispacecountspointedsmoothcohomology
0
0 comments X
read the original abstract

In this article we consider the moduli space of smooth $n$-pointed non-hyperelliptic curves of genus 3. In the pursuit of cohomological information about this space, we make $\mathbb{S}_n$-equivariant counts of its numbers of points defined over finite fields for $n \leq 7$. Combining this with results on the moduli spaces of smooth pointed curves of genus 0, 1 and 2, and the moduli space of smooth hyperelliptic curves of genus 3, we can determine the $\mathbb{S}_n$-equivariant Galois and Hodge structure of the ($\ell$-adic respectively Betti) cohomology of the moduli space of stable curves of genus 3 for $n \leq 5$ (to obtain $n \leq 7$ we would need counts of ``8-pointed curves of genus 2'').

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.