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Automorphisms of cubic surfaces without points
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2020-07-11 , DOI: 10.1142/s0129167x20500834
Constantin Shramov 1
Affiliation  

We classify finite groups acting by birational transformations of a nontrivial Severi–Brauer surface over a field of characteristic zero that are not conjugate to subgroups of the automorphism group. Also, we show that the automorphism group of a smooth cubic surface over a field [Formula: see text] of characteristic zero that has no [Formula: see text]-points is abelian, and find a sharp bound for the Jordan constants of birational automorphism groups of such cubic surfaces.

中文翻译:

无点三次曲面的自同构

我们通过非平凡 Severi-Brauer 曲面在不与自同构群的子群共轭的特征零场上的双有理变换来对起作用的有限群进行分类。此外,我们证明了在没有 [公式:参见文本] 点的特征零的域 [公式:参见文本] 上的平滑三次曲面的自同构群是阿贝尔的,并且找到了双有理的 Jordan 常数的锐界这种三次曲面的自同构群。
更新日期:2020-07-11
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