QUASIMODULARITY AND LARGE GENUS LIMITS OF SIEGEL-VEECH CONSTANTS
QUASIMODULARITY AND LARGE GENUS LIMITS OF SIEGEL-VEECH CONSTANTS
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DOI：
10.1090/jams/900
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发表时间：
2018-10-01
影响因子：
3.9
通讯作者：
Zagier, Don
中科院分区：
文献类型：
--
作者：
Chen, Dawei;Moeller, Martin;Zagier, Don
拟模形式首先在计数环面覆盖的背景下被系统地研究。在这里，我们表明，这些覆盖与Siegel-Veech权重的加权版本也提供了quasimodular形式。我们应用这一点来证明Eskin和Zorich的大属极限的Masur-Veech卷和Siegel-Veech常数。
Quasimodular forms were first studied systematically in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veech constants.