Siegel-Veech constants for strata of moduli spaces of quadratic differentials

Elise Goujard (1)

1 LMO - Laboratoire de Mathématiques d'Orsay

We present an explicit formula relating volumes of strata of meromorphic quadratic differentials with at most simple poles on Riemann surfaces and counting functions of the number of flat cylinders filled by closed geodesics in associated flat metric with singularities. This generalizes the result of Athreya, Eskin and Zorich in genus 0 to higher genera.

Mots clés: moduli spaces; volumes; Siegel-Veech constants; flat surfaces; quadratic differentials

Domaines: Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]

Elise Goujard. Siegel-Veech constants for strata of moduli spaces of quadratic differentials. Geometric And Functional Analysis, 2015, 25 (5), pp.1440-1492. ⟨hal-00995027v4⟩