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

2006/11/27 by Bergström, Jonas
#11G20 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0611815

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 \mathbbS_n-equivariant counts of its numbers of points defined over finite fields for n ≤ 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 \mathbbS_n-equivariant Galois and Hodge structure of the (ℓ-adic respectively Betti) cohomology of the moduli space of stable curves of genus 3 for n ≤ 5 (to obtain n ≤ 7 we would need counts of ``8-pointed curves of genus 2'').

Related

• Calculating cohomology groups of moduli spaces of curves via algebraic geometry
• Moduli spaces of curves with polynomial point counts
• Cohomology of the moduli space of non-hyperelliptic genus four curves
• Non-tautological cycles on moduli spaces of smooth pointed curves
• Divisors in the moduli spaces of curves