Siegel-Veech constants and Masur-Veech volumes: Connection to Intersection theory

Siegel-Veech常数测量台球桌上给定长度范围内闭合轨迹的渐近数。它们与平面模空间的体积比密切相关，即Masur-Veech体积。虽然以前这些Masur-Veech体积已经通过计数环面覆盖的渐近计算，最近建立的模空间上的相交理论的连接提供了一种新的方法，我们计划扩展到二次微分和更一般的所有仿射不变流形。

Siegel-Veech constants measure the asymptotic number of closed trajectories up to a given length bound on a billiard table. They are closely related to ratios of volumes on the moduli spaces of flat surfaces, the Masur-Veech volumes. While previously those Masur-Veech volumes have been computed through asymptotics of counting torus covers, connections to intersection theory on moduli spaces recently established provide a new approach that we plan to extend to quadratic differentials and more generally to all affine invariant manifolds.