Bijective Cremona transformations of the plane
Bijective Cremona transformations of the plane
复制标题
平面的双射克雷莫纳变换
DOI：
10.1007/s00029-022-00768-0
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Zimmermann, Susanna
中科院分区：
文献类型：
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作者：
Asgarli, Shamil;Lai, Kuan-Wen;Nakahara, Masahiro;Zimmermann, Susanna
我们研究有限域上射影平面的双有理自映射，该映射引起有理点集的排列。作为主要结果，我们证明在特征二的非素数有限域上不会出现奇数排列，这完成了 Cantat 发起的关于哪些排列可以通过这种方式实现的研究。我们证明中的主要成分包括双有理映射在群形共轭下的宇称不变性，以及此类映射组的生成器列表。
We study the birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we prove that no odd permutation arises over a non-prime finite field of characteristic two, which completes the investigation initiated by Cantat about which permutations can be realized this way. Main ingredients in our proof include the invariance of parity under groupoid conjugations by birational maps, and a list of generators for the group of such maps.