English

Affine surfaces with trivial Makar-Limanov invariant

Algebraic Geometry 2007-05-23 v1 Commutative Algebra

Abstract

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].

Keywords

Cite

@article{arxiv.0705.0334,
  title  = {Affine surfaces with trivial Makar-Limanov invariant},
  author = {Daniel Daigle},
  journal= {arXiv preprint arXiv:0705.0334},
  year   = {2007}
}

Comments

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