The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay
The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay
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DOI：
10.1090/jag/724
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发表时间：
2017-10
影响因子：
1.8
通讯作者：
B. Totaro
中科院分区：
文献类型：
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作者：
B. Totaro
我们证明了Kodaira消失定理在任意特征p>0的光滑Fano变量上失效。在这些变种中，我们首先给出非科恩-麦考利端点奇点的第一个例子。通过另一种方法，我们在特征2上构造了一个3维（最低可能）的终端奇点，它不是Cohen-Macaulay。
We show that the Kodaira vanishing theorem can fail on smooth Fano varieties of any characteristic p > 0 p>0 . Taking cones over some of these varieties, we give the first examples of terminal singularities which are not Cohen-Macaulay. By a different method, we construct a terminal singularity of dimension 3 (the lowest possible) in characteristic 2 which is not Cohen-Macaulay.