Automorphisms and periods of cubic fourfolds
Automorphisms and periods of cubic fourfolds
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DOI：
10.1007/s00209-021-02810-x
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发表时间：
2019-05
影响因子：
0.8
通讯作者：
R. Laza;Zhiwei Zheng
中科院分区：
文献类型：
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作者：
R. Laza;Zhiwei Zheng
我们对三次四重的辛自同构群进行了分类。主要输入是三次四重的整体Torelli定理和Leech格的不动点子格的分类。在我们的结果的亮点，我们注意到，有34个可能的辛自同构群，6个最大的情况。六个最大的情况下，对应于8个非同构，并孤立在模，立方fourfolds;其中六个以前确定的其他作者。最后，费马三次四重函数在所有光滑三次四重函数中具有自同构群（不一定是辛的）的最大可能阶（174，960）。
We classify the symplectic automorphism groups for cubic fourfolds. The main inputs are the global Torelli theorem for cubic fourfolds and the classification of the fixed-point sublattices of the Leech lattice. Among the highlights of our results, we note that there are 34 possible groups of symplectic automorphisms, with 6 maximal cases. The six maximal cases correspond to 8 non-isomorphic, and isolated in moduli, cubic fourfolds; six of them previously identified by other authors. Finally, the Fermat cubic fourfold has the largest possible order (174, 960) for the automorphism group (non-necessarily symplectic) among all smooth cubic fourfolds.