Arithmetic study of Calabi-Yau varieties with fibration

Calabi-Yau 品种纤维化的算术研究

• 批准号: 21540003
• 负责人: GOTO Yasuhiro
• 金额: $ 2.25万
• 依托单位: Hokkaido University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540003/
• 关键词: カラビ・ヤウ多様体; 数論幾何; ゼータ関数; L関数; モジュラリティ; 形式群; 代数幾何; 国際研究者交流; カナダ; 数論; デルサルト型多様体

We studied the arithmetic of Calabi-Yau threefolds with fibration by elliptic curves and/or K3 surfaces. The focus was put on Calabi-Yau threefolds of Delsarte type defined in a weighted projective space over a number field and also on Calabi-Yau threefolds considered by Voisin and Borcea in their construction of mirror symmetry. Taking into account the information of fibrations, we computed the cohomology, zeta functions and L-functions of such Calabi-Yau threefolds. We moreover obtained results on their modularity (automorphy) and on the height of their formal groups.

我们研究了Calabi-yau三倍的算术，并通过椭圆曲线和/或K3表面进行了振动。将重点放在Delsarte类型的Calabi-yau三倍上，该类型在一个数字字段的加权投影空间中定义，以及Voisin和Borcea在构建镜子对称性时考虑的Calabi-yau三倍。考虑到纤维化的信息，我们计算了此类calabi-yau三倍的共同体，Zeta功能和L功能。此外，我们还获得了它们的模块化（汽车）和正式组的高度的结果。

项目成果

(1)北海道教育大学研究者総覧 後藤泰宏の項目

(1) 北海道教育大学研究员后藤康宏的项目

Zeta-functions of Various Calabi-Yau threefolds

各种 Calabi-Yau 的 Zeta 函数三重

• 发表时间: 2009
• 作者: Goto;Yasuhiro
• 通讯作者: Yasuhiro

On K3 surfaces with involution

在包含对合的 K3 曲面上

• 发表时间: 2011
• 作者: Goto;Yasuhiro
• 通讯作者: Yasuhiro

On K3 Surfaces with Non-symplectic Involution

具有非辛对合的 K3 曲面

• 发表时间: 2011
• 作者: Goto;Yasuhiro
• 通讯作者: Yasuhiro

Calculations on K3 surfaces with involution

包含对合的 K3 曲面的计算

• 发表时间: 2011
• 作者: Goto;Yasuhiro
• 通讯作者: Yasuhiro