论文标题
孤儿卡拉比（Calabi-yau
Orphan Calabi-Yau threefold with arithmetic monodromy group
论文作者
论文摘要
我们研究了Calabi-yau三倍的单参数家族的Picard-fuchs运算符，而没有最大的一能单位单肌（\ emph {orphan operators}）。我们为所有孤儿的八八束PICARD-FUCHS运营商$ 4 $构建了理性的符号基础。结果，我们表明，所有双八个孤儿运算符的单型组都在$ \ mathrm {sp（4，\ mathbb {z}）}中密集，并确定所有这些元素的最大单位元素，除了一个。最后，我们证明了这些孤儿操作员之一的单型组是算术的。
We study monodromy groups of Picard-Fuchs operators of one-parameter families of Calabi-Yau threefolds without a point of Maximal Unipotent Monodromy (\emph{orphan operators}). We construct rational symplectic bases for the monodromy action for all orphan double octic Picard-Fuchs operators of order $4$. As a consequence we show that monodromy groups of all double octic orphan operators are dense in $\mathrm{Sp(4,\mathbb{Z})}$ and identify maximally unipotent elements in all of them, except one. Finally, we prove that the monodromy group of one of these orphan operators is arithmetic.
