Varieties of general type with doubly exponential asymptotics
Varieties of general type with doubly exponential asymptotics
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DOI：
10.1090/btran/125
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
L. Esser;B. Totaro;Chengxi Wang
中科院分区：
文献类型：
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作者：
L. Esser;B. Totaro;Chengxi Wang
我们构造光滑的投影品种的一般类型的最小的已知体积和其他最知名的消失plurigenes在高维。最佳体积边界预计会随着维度呈双指数衰减，我们的示例实现了此衰减率。我们还考虑了其他类型的品种的类似问题。例如，在每一个维度，我们猜想终端Fano品种的最小体积，和规范的卡-丘品种的最小体积。在每种情况下，我们的例子都表现出双指数行为。
We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with dimension, and our examples achieve this decay rate. We also consider the analogous questions for other types of varieties. For example, in every dimension we conjecture the terminal Fano variety of minimal volume, and the canonical Calabi-Yau variety of minimal volume. In each case, our examples exhibit doubly exponential behavior.