Toward the resolution of problems on algebraic varieties in positive characteristic

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540051
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tokyo University of Science
• Principal Investigator: Ito Hiroyuki 東京理科大学, 理工学部, 教授 (60232469)
• Co-Investigator(Renkei-kenkyūsha): HIROKADO MASAYUKI 広島市立大学, 大学院情報科学研究科, 講師 (40316138) ; SAITOU NATSUO 広島市立大学, 大学院情報科学研究科, 講師 (70382372)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 代数幾何学 / 特異点 / 正標数 / 楕円曲面 / K3曲面 / 群スキーム / 疑似乱数生成 / 非ケーラー幾何

Outline of Final Research Achievements

1) We classified elliptic K3 surfaces whose Mordell-Weil group have p-torsion. As a corollary, we found the strong relationship between the moduli space of such surfaces and deformation spaces of rational double points. 2) We solved the problems on the dual graph of wild quotient singularities. 3) By introducing the notion of pseudo-derivations, we consider quotient singularities not only by finite groups but by group schemes, which enable the unified treatment of various quotient singularities in positive characteristic. 4) We continued the evaluation of AST pseudo-random number generators. We also collect and consider the phenomena which give the evidences of the analogy between non-Kaeler geometry and positive characteristic algebraic geometry.

Free Research Field

代数学