## 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.

### MSC:

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

Mathematica
Full Text:

### References:

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