Cylinders over affine surfaces

Abstract

For an affine variety $S$ we consider the ring $AK(S),$ which is the intersection of the rings of constants of all locally-nilpotent derivations of the ring $\Cal {O}(S).$ We show that $AK(S\times {\mathbb{C}}^n)=AK(S)$ for a smooth affine surface $S$ with $H^2(S,\mathbb{Z})=\{0\}.$

14 pages, Ams-TeX