2005/12/07 by Adrien Dubouloz, Dubouloz, Adrien
Arts and Humanities · Mathematics · #14R10 #14R25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Historical Studies and Socio-cultural Analysis
paper · pdf · doi:10.48550/arxiv.math/0512152
openalex publication_date 2005/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Affine surfaces in ℂ3 defined by an equation of the form xnz-Q(x,y)=0 have been increasingly studied during the past 15 years. Of particular interest is the fact that they come equipped with an action of the additive group ℂ+ induced by such an action on the ambient space. The litterature of the last decade may lead one to believe that there are essentially no other of rational surfaces in ℂ3 with this property. In this note, we construct an explicit example of a surface nonisomorphic to a one of the above type but equipped with a free ℂ+-action induced by an action on ℂ3. We give an elementary and self-contained proof of this fact. As an application, we construct a wild but stably-tame automorphisme of ℂ3 which seems to be new.