2004/01/19 by Adrien Dubouloz, Dubouloz, Adrien
Mathematics · #14J26 #14R05 #14R20 #14R25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AG #msc:14J26 #msc:14R05 #msc:14R20 #msc:14R25
paper · pdf · doi:10.48550/arxiv.math/0401225
In this paper, we generalize the results on Danielewski surfaces to surfaces admitting certain A^1-fibration p:S-->X over the spectrum of a discrete valuation ring. We characterize among them the ones with a trivial Makar-Limanov invariant over an arbitrary algebraically closed field of caracteristic zero
openalex publication_date 2004/01/19 · arxiv created 2004/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a class of normal affine surfaces with additive group actions which contains in particular the Danielewski surfaces in \ba3 given by the equations xnz=P(y), where P is a nonconstant polynomial with simple roots. We call them Danielewski-Fieseler Surfaces. We reinterpret a construction of Fieseler \citeFie94 to show that these surfaces appear as the total spaces of certain torsors under a line bundle over a curve with an r-fold point. We classify Danielewski-Fieseler surfaces through labelled rooted trees attached to such a surface in a canonical way. Finally, we characterize those surfaces which have a trivial Makar-Limanov invariant in terms of the associated trees.