Tschirnhausen transformation of a cubic generic polynomial and a \(2\)-dimensional involutive Cremona transformation. (English) Zbl 1126.14018

The authors 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. The authors prove that the fixed field under the action of the transformation is purely transcendental over an arbitrary base field.


14E07 Birational automorphisms, Cremona group and generalizations
12F12 Inverse Galois theory


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