Cubic curves and totally geodesic subvarieties of moduli space

• 成果类型: Article
• 署名作者: McMullen, Curtis T.; Mukamel, Ronen E.; Wright, Alex
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.185.3.6
• 发表日期: 2017
• 页码: 957-990
• 关键词: teichmuller curves; veech surfaces; invariant; billiards

摘要

In this paper we present the first example of a primitive, totally geodesic subvariety F subset of M-g,M-n with dim(F) > 1. The variety we consider is a surface F subset of M-1,M-3 defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmuller curves in M-4, and new SL2(R)-invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.