1998/01/16 by Shulim Kaliman, Mikhail Zaidenberg, Kaliman, Shulim +1 · 3 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.math/9801076
39 Pages, LaTeX; a revised version with minor changes and corrections
openalex publication_date 1998/01/16 · arxiv created 1998/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface X ⊂ Ck+2 given by the equation uv=p(x1,...,xk) where p ∈ C[x1,...,xk], acts m-transitively on the smooth part regX of X for any m ∈ N. We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.