Geometry of orthogonal modular varieties

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K14158
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Ma Shouhei 東京工業大学, 理学院, 准教授 (80633255)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 直交型モジュラー多様体

Outline of Final Research Achievements

I studied the birational type of orthogonal modular varieties and the moduli spaces of pointed K3 surfaces. In particular, I proved that most orthogonal modular varieties are of general type in dimension greater than 20. As a byproduct I proved a conjecture of Gritsenko and Nikulin on reflective modular forms. For the moduli spaces of pointed K3 surfaces, I studied the transition point of Kodaira dimension. I also studied some topics related to Borcherds products, such as equivariant Gauss sum, quasi-pullback formula and a new product structure.

Free Research Field

代数幾何

Academic Significance and Societal Importance of the Research Achievements

直交型モジュラー多様体は代数幾何、数論、表現論が交わる豊かな研究対象である。本研究では直交型モジュラー多様体のいくつかの幾何学的性質を研究した。特に高次元でほとんど一般型になるという結果は、「大自然はやはり複雑で奥深い」ということをある意味定量的に示したものと言える。