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

Elise Goujard (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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

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

Elise Goujard. Siegel-Veech constants for strata of moduli spaces of quadratic differentials. 2014. ⟨hal-00995027v2⟩