# Journées de Géométrie Algébrique Poitiers-Bordeaux

24-25 November 2016
Poitiers
Europe/Paris timezone

## Volume of complex hyperbolic structures on moduli spaces of genus zero curves

24 Nov 2016, 11:45
50m
0-6 (Poitiers)

Board: 3
Exposé de 50 min

### Speaker

Prof. Vincent Koziarz

### Description

(joint work with D. M. Nguyen): I will show that the complex hyperbolic metrics defined by Deligne-Mostow and Thurston on the moduli space of genus $0$ curves with $n$ marked points $M_{0,n}$ are singular Kaehler-Einstein metrics when $M_{0,n}$ is embedded in its Deligne-Mumford-Knudsen compactification. As a consequence, I will obtain a formula computing the volume of $M_{0,n}$ with respect to these metrics using intersection of boundary divisors of its compactification. In the case when the weights parametrizing the complex hyperbolic structures are rational, following an idea of Y. Kawamata, I will show that the associated metrics actually represent the first Chern class of some line bundles on the compactification of $M_{0,n}$, from which other formulas computing the same volumes will be derived.

### Presentation Materials

There are no materials yet.