发表机构
Jagiellonian University（雅盖隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了一个Mordell-Weil秩为十二的平坦椭圆纤维化Calabi-Yau三维流形，其Hodge数为(25,1)，通过Kummer曲面出发并给出十二个独立截面及crepant解消。
AI 中文摘要
我们构造了一个光滑射影Calabi-Yau三维流形，其具有Mordell-Weil秩为十二的平坦椭圆纤维化，且Hodge数$(h^{1,1},h^{2,1})=(25,1)$。该构造始于与固定椭圆曲线和四级模族乘积相关的Kummer曲面。该三维流形双有理于$\mathbb{P}(\mathcal{O}_{\mathbb{P}^1}(3)^{\oplus2}\oplus\mathcal{O}_{\mathbb{P}^1}(4)\oplus\mathcal{O}_{\mathbb{P}^1})$中的反典范四次曲面。我们给出了十二个独立截面，并构造了相应Weierstrass模型的射影crepant解消。
英文摘要
We construct a smooth projective Calabi--Yau threefold with a flat elliptic fibration of Mordell--Weil rank twelve and Hodge numbers $(h^{1,1},h^{2,1})=(25,1)$. The construction starts from the Kummer surfaces associated with the products of a fixed elliptic curve and the level-four modular family. The threefold is birational to an anticanonical quartic in $\mathbb{P}(\mathcal{O}_{\mathbb{P}^1}(3)^{\oplus2}\oplus\mathcal{O}_{\mathbb{P}^1}(4)\oplus\mathcal{O}_{\mathbb{P}^1})$. We give twelve independent sections and construct a projective crepant resolution of the associated Weierstrass model.
Comments16 pages; exact verification code included as ancillary files
