On polynomials in three variables annihilated by two locally nilpotent derivations

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• 作者：Daniel Daigle
• 关键词：Locally nilpotent derivations ; Group actions ; Danielewski surfaces ; Affine surfaces ; Polynomial automorphisms ; Variables
• 刊名：Journal of Algebra
• 出版年：2007
• 期刊代码：69_00218693
• 类别：mt
• 出版时间：1 April 2007
• 卷：310
• 期：1
• 页码：303-324
• 文件大小：249 K

摘要

Let B be a polynomial ring in three variables over an algebraically closed field k of characteristic zero. We are interested in irreducible polynomials fB satisfying the following condition: there exist nonzero locally nilpotent derivations such that ker(D₁)≠ker(D₂) and D₁(f)=0=D₂(f). The main result asserts that a nonconstant polynomial fB satisfies the above requirement if and only if its “generic fiber” k(f)_k[f]B is isomorphic, as an algebra over the field K=k(f), to K[X,Y,Z]/(XY−φ(Z)) for some nonconstant φ(Z)K[Z].