Volumes of moduli spaces of flat surfaces

2020/04/07 by Adrien Sauvaget, Sauvaget, Adrien · 5 citations
Mathematics · #14C17 #14H10 #14H51 #30F45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2004.03198

openalex publication_date 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the moduli spaces of flat surfaces with prescribed conical singularities. Veech showed that these spaces are diffeomorphic to the moduli spaces of marked Riemann surfaces, and endowed with a natural volume form depending on the orders of the singularities. We show that the volumes of these spaces are finite. Moreover we show that they are explicitely computable by induction on the Euler characteristics of the punctured surface for almost all orders of the singularities.

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