Tschirnhausen transformation of a cubic generic polynomial and a 2-dimensional involutive Cremona transformation

被引：6
|
作者：
Hoshi, Akinari
Miyake, Katsuya
机构：
[1] Waseda Univ, Dept Math, Sch Educ, Shinjuku Ku, Tokyo 1698050, Japan
[2] Waseda Univ, Dept Math Sci, Sch Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan
来源：
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2007年 / 83卷 / 03期
关键词：
tschirnhausen transformation; cubic generic polynomial; field isomorphism problem; involutive Cremona transformation; general Noether problem;
D O I：
10.3792/pjaa.83.21
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the field isomorphism problem for a cubic generic polynomial X-3 + sX + s via Tschirnhausen transformation. Through this process, there naturally appears a 2-dimensional involutive Cremona transformation. We show that the fixed field under the action of the transformation is purely transcendental over an arbitrary base field.
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页码：21 / 26
页数：6
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