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Mathematics > Algebraic Geometry

Title: K3 surfaces with real or complex multiplication

Authors: Eva Bayer-Fluckiger, Bert van Geemen, Matthias Schütt
(Submitted on 8 Jan 2024 (v1), last revised 26 Mar 2024 (this version, v2))
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 hyperk\"ahler manifolds.
Comments: 32 pages; v2: major extension covering also higher-dimensional hyperk\"ahler manifolds and possible Picard lattices
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
Cite as: arXiv:2401.04072 [math.AG]
  (or arXiv:2401.04072v2 [math.AG] for this version)

Submission history

From: Matthias Schütt [view email]
[v1] Mon, 8 Jan 2024 18:18:33 GMT (13kb)
[v2] Tue, 26 Mar 2024 20:31:18 GMT (29kb)
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