The group of Cremona transformations generated by linear maps and the standard involution
The group of Cremona transformations generated by linear maps and the standard involution
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由线性映射和标准对合生成的克雷莫纳变换组
DOI：
10.5802/aif.2999
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Isac Hed'en
中科院分区：
文献类型：
--
作者：
J. Blanc;Isac Hed'en
本文研究由 $n$ 维射影空间的自同构和 $n$ 次标准双有理对合生成的群。该群中的每个元素仅收缩有理超曲面，但在奇数维中，存在不属于该群的具有此性质的简单元素。给出了群元素的几何性质，以及其与单项式变换的交集的描述。
This article studies the group generated by automorphisms of the projective space of dimension $n$ and by the standard birational involution of degree $n$. Every element of this group only contracts rational hypersurfaces, but in odd dimension, there are simple elements having this property which do not belong to the group. Geometric properties of the elements of the group are given, as well as a description of its intersection with monomial transformations.