Open Access
October 2008 A rationality problem of some Cremona transformation
Akinari Hoshi, Ming-chang Kang
Proc. Japan Acad. Ser. A Math. Sci. 84(8): 133-137 (October 2008). DOI: 10.3792/pjaa.84.133

Abstract

In this note we give a new approach to the rationality problem of some Cremona transformation. Let k be any field, k(x,y) be the rational function field of two variables over k. Let σ be a k-automorphism of k(x,y) defined by σ(x)=x(3x9yy2)3(27x+2x2+9xy+2xy2y3)2,σ(y)=(3x+y2)(3x9yy2)27x+2x2+9xy+2xy2y3. Theorem. The fixed field k(x,y)σ is rational (= purely transcendental) over k. Embodied in a new proof of the above theorem are several general guidelines for solving the rationality problem of Cremona transformations, which may be applied elsewhere.

Citation

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Akinari Hoshi. Ming-chang Kang. "A rationality problem of some Cremona transformation." Proc. Japan Acad. Ser. A Math. Sci. 84 (8) 133 - 137, October 2008. https://doi.org/10.3792/pjaa.84.133

Information

Published: October 2008
First available in Project Euclid: 6 October 2008

zbMATH: 1162.14009
MathSciNet: MR2457800
Digital Object Identifier: 10.3792/pjaa.84.133

Subjects:
Primary: 12F20 , 13A50 , 14E07 , 14E08

Keywords: Cremona transformations , linear actions , monomial group actions , rationality problem

Rights: Copyright © 2008 The Japan Academy

Vol.84 • No. 8 • October 2008
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