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

Siegel-Veech 常数和 Masur-Veech 体积：与交集理论的联系

• 批准号: 275218485
• 负责人: Professor Dr. Martin Möller
• 金额: --
• 依托单位: Math Department
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/275218485?language=en
• 关键词: Siegel; Veech; constants; Masur; volumes

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.

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。