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March 2007 Tschirnhausen transformation of a cubic generic polynomial and a $2$-dimensional involutive Cremona transformation
Akinari Hoshi, Katsuya Miyake
Proc. Japan Acad. Ser. A Math. Sci. 83(3): 21-26 (March 2007). DOI: 10.3792/pjaa.83.21

Abstract

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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Akinari Hoshi. Katsuya Miyake. "Tschirnhausen transformation of a cubic generic polynomial and a $2$-dimensional involutive Cremona transformation." Proc. Japan Acad. Ser. A Math. Sci. 83 (3) 21 - 26, March 2007. https://doi.org/10.3792/pjaa.83.21

Information

Published: March 2007
First available in Project Euclid: 9 April 2007

zbMATH: 1126.14018
MathSciNet: MR2317305
Digital Object Identifier: 10.3792/pjaa.83.21

Subjects:
Primary: 12F12, 12F20, 14E07, 14E08

Rights: Copyright © 2007 The Japan Academy

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Vol.83 • No. 3 • March 2007
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