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arXiv · 2401.04072

K3 surfaces with real or complex multiplication

Eva Bayer-Fluckiger·Bert van Geemen·Matthias Schütt
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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.

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Eva Bayer-Fluckiger, Bert van Geemen, Matthias Schütt. 2024-01-08. K3 surfaces with real or complex multiplication. https://arxiv.org/abs/2401.04072

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