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arXiv · 2511.19970

Non-projective K3 surfaces with real or Salem multiplication

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

We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperk\"ahler manifolds). We show that they are either totally real fields or number fields generated by Salem numbers. This is unlike the projective case, where the endomorphism fields are either totally real or CM. We also develop precise existence criteria and explore the relations to number theory and dynamics.

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Eva Bayer-Fluckiger, Bert van Geemen, Matthias Schütt. 2025-11-25. Non-projective K3 surfaces with real or Salem multiplication. https://arxiv.org/abs/2511.19970

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