A Rationality Problem of Some Cremona Transformation
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چکیده
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(3x− 9y − y) (27x+ 2x + 9xy + 2xy − y) , σ(y) = −(3x+ y)(3x− 9y − y) 27x+ 2x + 9xy + 2xy − y . Theorem. The fixed field k(x, y) is rational (= purely transcendental) over k. Embodied in the proof of the above theorem are several general guidelines for solving the rationality problem of Cremona transformations, which may be applied elsewhere.
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تاریخ انتشار 2008