Tschirnhausen transformation of a cubic generic polynomial and a \(2\)-dimensional involutive Cremona transformation (Q2381152)

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.