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].
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