Abstract
We study a class of normal affine surfaces, with additive group actions, which contains in particular the Danielewski surfaces in A3 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 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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dubouloz, A. Danielewski–Fieseler surfaces. Transformation Groups 10, 139–162 (2005). https://doi.org/10.1007/s00031-005-1004-x
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00031-005-1004-x