Volumes of strata of moduli spaces of quadratic differentials: getting explicit values

Goujard, Elise

Annales de l'Institut Fourier, Tome 66 (2016) no. 6, pp. 2203-2251.

Les volumes de strates de différentielles abéliennes ou quadratiques jouent un rôle important dans l’étude de la dynamique sur les surfaces plates, en lien avec la dynamique des billards polygonaux. Dans cet article nous utilisons toutes les approches connues pour calculer les volumes dans le cas quadratique et fournissons des valeurs explicites pour les volumes de toutes les strates de différentielles quadratiques méromorphes à pôles au plus simples jusqu’en dimension 10.

The volumes of strata of Abelian or quadratic differentials play an important role in the study of dynamics on flat surfaces, related to dynamics in polygonal billiards. This article applies all known approaches to compute volumes in the quadratic case and provides explicit values of volumes of the strata of meromorphic quadratic differentials with at most simple poles in all dimensions up to 10.

Classification : 30F30, 14N10, 32G15
Keywords: flat surfaces, quadratic differentials, volumes, strata
Mot clés : surfaces plates, différentielles quadratiques, volumes, strates

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