Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials

• 成果类型: Article
• 署名作者: Chen, Dawei; Moeller, Martin; Sauvaget, Adrien; Zagier, Don
• 署名单位: Boston College; Goethe University Frankfurt; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00969-4
• 发表日期: 2020
• 页码: 283-373
• 关键词: principal boundary; billiards; transformations; numbers; strata

摘要

We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained using intersection theory on strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel-Veech constants for all strata. We also show that the same results hold for the spin and hyperelliptic components of the strata.