Affine surfaces with trivial Makar-Limanov invariant

Details Affine surfaces with trivial Makar-Limanov invariant Affine surfaces with trivial Makar-Limanov invariant

2007-05-02

arxiv.org/abs/0705.0334v1

Mathematics

Algebraic Geometry

12 pages. See also http://aix1.uottawa.ca/~ddaigle/index.html

Scientific paper

We study the class of 2-dimensional affine k-domains R satisfying ML(R) = k, where k is an arbitrary field of characteristic zero. In particular, we obtain the following result: Let R be a localization of a polynomial ring in finitely many variables over a field of characteristic zero. If ML(R) = K for some field K included in R and such that R has transcendence degree 2 over K, then R is K-isomorphic to K[X,Y,Z]/(XY-P(Z)) for some nonconstant polynomial P(Z) in K[Z].

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