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

Abstract

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 reviews all known ways 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 low dimensions.

arXiv comment43 pages, 13 figures. To appear in Ann. Inst. Fourier. arXiv admin note: text overlap with arXiv:1405.5899