2013/11/05 by Frank Kutzschebauch, Kutzschebauch, Frank, Matthias Leuenberger +1
Mathematics · #(32M05 #14R10 #14R20) #32M17 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14R10 #msc:32M17
paper · pdf · doi:10.48550/arxiv.1311.1075
20 pages
arxiv created 2014/11/24 · arxiv updated 2014/11/25
We give a full description of the Lie algebra generated by locally nilpotent derivations (short LNDs) on smooth Danielewski surfaces Dp given by xy=p(z). In case deg(p)≥ 3 it turns out to be not the whole Lie algebra VFalgω(Dp) of volume preserving algebraic vector fields, thus answering a question posed by Lind and the first author. Also we show algebraic volume density property (short AVDP) for a certain homology plane, a homogeneous space of the form SL2 (ℂ) /N, where N is the normalizer of the maximal torus and another related example. At the end of the paper we show by example that for the group of holomorphic automorphisms of a Stein manifold (endowed with c.-o. topology) the connected component and the path-connected component of the identity may not coincide.