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Transitivity of automorphism groups of Gizatullin surfaces

2013/04/26 by Sergei Kovalenko, Kovalenko, Sergei · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1304.7116

openalex publication_date 2013/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the automorphism group of a certain subclass of smooth Gizatullin surfaces with a distinguished and rigid extended divisor is generated by automorphisms of A1-fibrations. Moreover, such surfaces provide examples of smooth Gizatullin surfaces with a non-transitive action of the automorphism group. Thus, they represent counterexamples to Gizatullin's conjecture. For such surfaces we give explicit orbits of the natural action of the automorphism group in some special cases. Further, we present their automorphism groups as amalgamated products of two subgroups.

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