2006/05/19 by Peter Ebenfelt, P. Ebenfelt, Ebenfelt, P. +6
Mathematics · #32H02 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.CV #msc:32H02
paper · pdf · doi:10.48550/arxiv.math/0605540
arxiv created 2006/05/19 · openalex publication_date 2006/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce new biholomorphic invariants for real-analytic hypersurfaces in 2-dimensional complex space and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new invariants, guaranteeing that the stability group is finite, and give (sharp) bounds on the cardinality of the stability group in this case. We also give a sufficient condition for the stability group to be trivial. The main technical tool developed in this paper is a complete (formal) normal form for a certain class of hypersurfaces. As a byproduct, a complete classification, up to biholomorphic equivalence, of the finite type hypersurfaces in this class is obtained.