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March 2012 Simplicial volume of moduli spaces of Riemann surfaces
Lizhen Ji
J. Differential Geom. 90(3): 413-437 (March 2012). DOI: 10.4310/jdg/1335273390

Abstract

Motivated by results on the simplicial volume of locally symmetric spaces of finite volume, in this note, we observe that the simplicial volume of the moduli space $M_{g,n}$ is equal to $0$ if $g \ge 2$; $g = 1$, $n \ge 3$; or $g = 0$, $n \ge 6$; and the orbifold simplicial volume of $M_{g,n}$ is positive if $g = 1, n = 0, 1; g = 0, n = 4$. We also observe that the simplicial volume of the Deligne-Mumford compactification of $M_{g,n}$ is equal to $0$, and the simplicial volumes of the reductive Borel-Serre compactification of arithmetic locally symmetric spaces $\Gamma\backslash X$ and the Baily-Borel compactification of Hermitian arithmetic locally symmetric spaces $\Gamma\backslash X$ are also equal to $0$ if the $\mathbb{Q}$-rank of $\Gamma\backslash X$ is at least $3$ or if $\Gamma\backslash X$ is irreducible and of $\mathbb{Q}$-rank 2.

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Lizhen Ji. "Simplicial volume of moduli spaces of Riemann surfaces." J. Differential Geom. 90 (3) 413 - 437, March 2012. https://doi.org/10.4310/jdg/1335273390

Information

Published: March 2012
First available in Project Euclid: 24 April 2012

zbMATH: 1254.30074
MathSciNet: MR2916042
Digital Object Identifier: 10.4310/jdg/1335273390

Rights: Copyright © 2012 Lehigh University

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Vol.90 • No. 3 • March 2012
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