Arithmetic Study of Calabi-Yau threefolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04771
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hokkaido University of Education
• Principal Investigator: Goto Yasuhiro 北海道教育大学, 教育学部, 教授 (40312425)
• Research Collaborator: YUI Noriko クイーンズ大学, 数理科学研究科, 教授
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: ３次元カラビ・ヤウ多様体 / 形式群 / 数論幾何 / デルサルト型多様体 / ミラー対称性 / 国際研究者交流（カナダ）

Outline of Final Research Achievements

We studied the arithmetic of Calabi-Yau threefolds defined over a field of positive characteristic by placing a focus on their formal groups. The main objects of our study are weighted Delsarte threefolds and Calabi-Yau threefolds of Borcea-Voisin type. For such threefolds, we obtained a lot of new numerical data about the height of their formal groups and described relationships between the height of formal groups and several geometric properties of Calabi-Yau threefolds, such as the Hodge numbers. As an application, we investigated the formal groups of Calabi-Yau threefolds relating each other by mirror symmetry.

Free Research Field

数論的代数幾何