Algebraic density property of Danilov-Gizatullin surfaces

2010/09/21 by Fabrizio Donzelli, Donzelli, Fabrizio · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #math.CV

paper · pdf · doi:10.48550/arxiv.1009.4209

12 pages

arxiv created 2010/09/21 · openalex publication_date 2010/09/21 · arxiv updated 2010/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Danilov-Gizatullin surface is an affine surface V which is the complement of an ample section S of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism class of V depends only on the self-intersection number S². In this paper we apply their theorem to present V as the quotient of an affine threefold by a torus action, and to prove that the Lie algebra generated by the complete algebraic vector fields on V coincides with the set of all algebraic vector fields.

Citations

• Density property for hypersurfaces UV = P( X)

Cited by

• Makar-Limanov invariant, Derksen invariant, flexible points

Related

• On the Danilov-Gizatullin Isomorphism Theorem
• The density property for Gizatullin surfaces with reduced degenerate\n fibre
• Lie algebra generated by locally nilpotent derivations on Danielewski surfaces
• The classification of complex algebraic surfaces
• Complete Algebraic Vector Fields on Danielewski Surfaces