Complex hyperbolic volume and intersection of boundary divisors in moduli spaces of pointed genus zero curves.
Language
en
Article de revue
This item was published in
Annales Scientifiques de l'École Normale Supérieure. 2018
Société mathématique de France
English Abstract
We show that the complex hyperbolic metrics defined by Deligne-Mostow and Thurston on M0,n are singular K\"ahler-Einstein metrics when $M_{0,n}$ is embedded in the Deligne-Mumford-Knudsen compactification$\bar{M}_{0,n}$. ...Read more >
We show that the complex hyperbolic metrics defined by Deligne-Mostow and Thurston on M0,n are singular K\"ahler-Einstein metrics when $M_{0,n}$ is embedded in the Deligne-Mumford-Knudsen compactification$\bar{M}_{0,n}$. As a consequence, we obtain a formula computing the volumes of $M_{0,n}$ with respect to these metrics using intersection of boundary divisors of $\bar{M}_{0,n}$. In the case of rational weights, following an idea of Y. Kawamata, we show that these metrics actually represent the first Chern class of some line bundles on $\bar{M}_{0,n}$, from which other formulas computing the same volumes are derived.Read less <
Origin
Hal imported