论文标题
大索引的卡拉比（Calabi-Yau）品种
Calabi-Yau varieties of large index
论文作者
论文摘要
如果其规范除数为$ {\ bf q} $，请致电投影品$ x $ calabi-yau-线性等同于零。最小的正整数$ m $，$ mk_x $线性等效于零，称为$ x $的索引。我们构建具有高维度最大的已知指数的Calabi-yau品种。在我们的示例中，该索引随维度呈双重增长。我们猜想我们的示例具有最大的指数，并具有低维度的支持证据。这些示例是通过从我们的Calabi-yau品种的镜像对称性获得的，具有大量的小体积。我们还提供了几个相关问题的示例，包括具有较大的Orbifold Betti数字或最小对数差异的Calabi-Yau品种。
Call a projective variety $X$ Calabi-Yau if its canonical divisor is ${\bf Q}$-linearly equivalent to zero. The smallest positive integer $m$ with $mK_X$ linearly equivalent to zero is called the index of $X$. We construct Calabi-Yau varieties with the largest known index in high dimensions. In our examples, the index grows doubly exponentially with dimension. We conjecture that our examples have the largest possible index, with supporting evidence in low dimensions. The examples are obtained by mirror symmetry from our Calabi-Yau varieties with an ample Weil divisor of small volume. We also give examples for several related problems, including Calabi-Yau varieties with large orbifold Betti numbers or small minimal log discrepancy.
