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

TL;DR

This paper derives an explicit formula connecting the volumes of moduli space strata of quadratic differentials with counting functions for flat cylinders, extending previous genus 0 results to higher genera.

Contribution

It generalizes existing formulas for genus 0 to higher genera, linking volumes of moduli spaces with cylinder counting functions for quadratic differentials.

Findings

Explicit formula relating volumes and cylinder counts

Extension of genus 0 results to higher genera

Provides tools for studying flat surfaces with singularities

Abstract

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