Cohomology of moduli spaces of curves of genus three via point counts
2008 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 622, 155-187 p.Article in journal (Refereed) Published
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 S-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 S-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'').
Place, publisher, year, edition, pages
2008. Vol. 622, 155-187 p.
FINITE-FIELDS; ABELIAN SURFACES; LOCAL SYSTEMS
IdentifiersURN: urn:nbn:se:kth:diva-6130DOI: 10.1515/CRELLE.2008.068ISI: 000260245900005ScopusID: 2-s2.0-46649104448OAI: oai:DiVA.org:kth-6130DiVA: diva2:10753
QC 201007012006-09-182006-09-182012-04-14Bibliographically approved