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Inversion of series and the cohomology of the moduli spaces $\scr M\sb 0,n\sp δ$
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
CNRS.
2010 (English)In: Motives, quantum field theory, and pseudodifferential operators, American Mathematical Society (AMS), 2010, Vol. 12, 119-126 p.Chapter in book (Other academic)
Abstract [en]

For $n\geq 3$, let $\mathcal{M}_{0,n}$ denote the moduli space of genus 0 curves with $n$ marked points, and $\overline{\mathcal{M}}_{0,n}$ its smooth compactification. A theorem due to Ginzburg, Kapranov and Getzler states that the inverse of the exponential generating series for the Poincar\'e polynomial of $H^{\bullet}(\mathcal{M}_{0,n})$ is given by the corresponding series for $H^{\bullet}(\overline{\mathcal{M}}_{0,n})$. In this paper, we prove that the inverse of the ordinary generating series for the Poincar\'e polynomial of $H^{\bullet}(\mathcal{M}_{0,n})$ is given by the corresponding series for $H^{\bullet}(\mathcal{M}^{\delta}_{0,n})$, where $\mathcal{M}_{0,n}\subset \mathcal{M}^{\delta}_{0,n} \subset \overline{\mathcal{M}}_{0,n}$ is a certain smooth affine scheme.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2010. Vol. 12, 119-126 p.
Series
Motives, quantum field theory, and pseudodifferential operators
National Category
Geometry
Identifiers
URN: urn:nbn:se:kth:diva-48390OAI: oai:DiVA.org:kth-48390DiVA: diva2:463655
Note
QS 2011Available from: 2011-12-10 Created: 2011-11-17 Last updated: 2012-01-18Bibliographically approved

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