Pseudo-automorphisms of rational threefolds and Kummer surfaces

2024/01/15 by Zhuang He, He, Zhuang
Mathematics · #14E07 (Primary) 14J28 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2401.07948

openalex publication_date 2024/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kummer surfaces are special quartic surfaces that admit 16 nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kondō, and as a continuation of the recent result by He and Yang, we lift 45 classically known automorphisms of Kummer surfaces to pseudo-automorphisms of a threefold, the blow-up of ℙ³ along 6 points and 15 lines. We give a description of a fundamental domain of the group generated by all the known pseudo-automorphisms on this threefold.

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