Complex hyperbolic volume and intersection of boundary divisors in moduli spaces of pointed genus zero curves.
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en
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Annales Scientifiques de l'École Normale Supérieure. 2018
Société mathématique de France
Resumen en inglés
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$\bar{M}_{0,n}$. ...Leer más >
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.< Leer menos
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