| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| 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.
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