Constructing Highly Symmetric Compact Manifolds and Algebraic Varieties

2023/04/20 by Dávid R. Szabó, Szabó, Dávid R. · 1 citation
Mathematics · #14E07 #14K25 #19L64 #20D15 (Secondary) #57S17 (Primary) 57S25 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2304.10366

openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

For every algebraically closed field k and natural number r, we construct several algebraic varieties (over k) whose birational automorphism group contains every finite nilpotent group of class at most 2, rank at most r whose order is coprime to the characteristic of k. This construction is sharp in characteristic 0, i.e. up to bounded extension, the set of groups from the statement cannot be replaced by a larger one. Using similar main ideas (with different technical details), for every r, we construct several compact manifolds whose diffeomorphism groups contain every finite nilpotent group of class at most 2, rank at most r. This result answers a question of Mundet~i~Riera affirmatively and is conjecturally sharp up to bounded extension.

Cited by

• Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds

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