Curvatures of moduli space of curves and applications

2013/12/25 by Kefeng Liu, Xiaofeng Sun, Liu, Kefeng +5 · 1 citation
Mathematics · #14K10 #32C10 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1312.6932

openalex publication_date 2013/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this paper, we investigate the geometry of the moduli space of curves by using the curvature properties of direct image sheaves of vector bundles. We show that the moduli space (M_g, ω_WP) of curves with genus g>1 has dual-Nakano negative and semi-Nakano-negative curvature, and in particular, it has non-positive Riemannain curvature operator and also non-positive complex sectional curvature. As applications, we prove that any submanifold in M_g which is totally geodesic in A_g with finite volume must be a ball quotient.

Citations

• The Torelli locus and special subvarieties

Cited by

• Isotriviality of families of curves parametrized by A_g(n)

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