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- W389614557 abstract "Abstract. A “rational” version of the strengthened form of the Com-muting Derivation Conjecture, in which the assumption of commuta-tivity is dropped, is proved. A systematic method of constructing inany dimension greater than 3 the examples answering in the negative aquestion by M. El Kahoui is developed. 1. IntroductionThroughout this paper k stands for an algebraically closed field of char-acteristic zero which serves as domain of definition for each of the algebraicvarieties considered below.Recall that an element c of the polynomial ring k[x 1 ,...,x n ] in variablesx 1 ,...,x n with coefficients in k is called a coordinate if there are the elementst 1 ,...,t n−1 ∈ k[x 1 ,...,x n ] such thatk[c,t 1 ,...,t n−1 ] = k[x 1 ,...,x n ](see, e.g.,[vdE 00]). Every coordinate is irreducible and, if x 1 ,...,x n are thestandard coordinate functions on the affine space A n , then the zero locus{c = 0} of c in A n is isomorphic to A n−1 . The converse is claimed by theclassicalAbhyankar–Sathaye Conjecture. If f ∈ k[x" @default.
- W389614557 created "2016-06-24" @default.
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- W389614557 date "2014-09-01" @default.
- W389614557 modified "2023-09-28" @default.
- W389614557 title "AROUND THE ABHYANKAR-SATHAYE CONJECTURE" @default.
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