K3 surfaces with real or complex multiplication

2024/01/08 by Eva Bayer-Fluckiger, Bert van Geemen, Bayer-Fluckiger, Eva +3 · 1 citation
Mathematics · #14C30 #14J28 (primary) #14J42 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14C30 #msc:14J28 #msc:14J42

paper · pdf · doi:10.48550/arxiv.2401.04072

31 pages; v4 corrects Lem 2.3, Theorem 8.1 and the proof of Corollary 8.2; main results unaffected; to appear in Algebraic Geometry

arxiv created 2026/07/31 · arxiv updated 2026/08/04

Abstract

Let E be a totally real number field of degree d and let m \geqslant 3 be an integer. We show that if md \leqslant 21 then there exists an (m-2)-dimensional family of complex projective K3 surfaces with real multiplication by E. Analogous results are proved for CM number fields and also for all known higher-dimensional hyperkähler manifolds.

Cited by

• Non-projective K3 surfaces with real or Salem multiplication

Related

• Explicit families of K3 surfaces having real multiplication
• K3 surfaces with maximal complex multiplication
• Non-projective K3 surfaces with real or Salem multiplication
• Real and complex multiplication on K3 surfaces via period integration
• Complex multiplication and Brauer groups of K3 surfaces