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About Abhyankar’s conjectures on space lines. (English) Zbl 0594.14025

In this note it is shown that there exists an automorphism of the affine space \({\mathbb{A}}^ 3\), sending the quintic curve \((t+t^ 5\), \(t^ 4\), \(t^ 3)\) into a straight line. - This partially answers a question raised by S. S. Abhyankar [in Proc. int. Symp. algebraic Geometry, Kyoto 1977, 249-414 (1977; Zbl 0408.14010)].
Reviewer: M.Raimondo

MSC:

14H45 Special algebraic curves and curves of low genus
14A25 Elementary questions in algebraic geometry

Citations:

Zbl 0408.14010
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References:

[1] S.S. Abhyankar , On the semigroup of a meromorphic curve (Part 1) , Intl. Symp. on Algebraic Geometry , Kyoto ( 1977 ), pp. 249 - 414 . MR 578864 | Zbl 0408.14010 · Zbl 0408.14010
[2] S.S. Abhankar , Algebraic space curves , Les Presses de l’Université de Montréal , 1971 . MR 399109 | Zbl 0245.14009 · Zbl 0245.14009
[3] P.C. Craighero , Osservazioni sopra alcuni esempi di curve dello spazio A3k isomorfe a rette , Bollettino U.M.I. , ( 6 ) 4-B ( 1982 ), pp. 1199 - 1216 . Zbl 0504.14024 · Zbl 0504.14024
[4] A. Sathaye , On linear planes , Proceedings of the American Mathematical Society, Vol. 56 (April 1976 ), pp. 1 - 7 . MR 409472 | Zbl 0345.14013 · Zbl 0345.14013 · doi:10.2307/2041561
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