Stratifications and foliations on the moduli space of abelian varieties

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800008
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Yokohama National University
• Principal Investigator: Harashita Shushi 横浜国立大学, 大学院環境情報研究院, 准教授 (70396852)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 代数幾何学 / アーベル多様体 / モジュライ空間 / p-可除群 / Deligne-Lusztig多様体 / 超特別曲線 / 最大曲線

Outline of Final Research Achievements

The moduli space of abelian varieties has many applications in algebra. The aim of this research is to investigate the stratifications and the foliations on the space in positive characteristic. We succeeded in giving a new criterion for the affineness of the distinguished Deligne-Lusztig varieties, which have similar structures as the Ekedahl Oort strata on the moduli space of abelian varieties. Moreover, Momonari Kudo and I enumerated superspecial curves of genus 4 in characteristic at most 7. Particularly we proved the non-existence of superspecial curves of genus 4 in characteristic 7 (a negative answer to a question by Ekedahl in 1987). Besides, we obtained results on p-divisible groups with saturated Newton polygons and got some new knowledge via a collaboration with Nobuhiro Higuchi.

Free Research Field

代数幾何学