Cohomology of moduli spaces of curves of genus three via point counts
| dc.creator | Bergström, Jonas | |
| dc.date | 2006-11-27 | |
| dc.date | 2007-06-05 | |
| dc.date.accessioned | 2026-07-07T08:08:27Z | |
| dc.date.available | 2026-07-07T08:08:27Z | |
| dc.description | 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''). | |
| dc.description | 25 pages, shortened version | |
| dc.identifier | https://arxiv.org/abs/math/0611815 | |
| dc.identifier | http://arxiv.org/abs/math/0611815 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131267 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H10, 11G20 | |
| dc.title | Cohomology of moduli spaces of curves of genus three via point counts | |
| dc.type | text |