Quartic K3 surfaces without nontrivial automorphisms

2005/11/22 by Ronald van Luijk, van Luijk, Ronald
Mathematics · #14G05 #14J28 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0511542

openalex publication_date 2005/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any field k of characteristic at most 5 we exhibit an explicit smooth quartic surface in projective threespace over k with trivial automorphism group over the algebraic closure of k. We also show how this can be extended to higher characteristics. Over the rationals we construct an example on which the set of rational points is Zariski dense.

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