Non-projective K3 surfaces with real or Salem multiplication
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911284862124032 |
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| author | Bayer-Fluckiger, Eva van Geemen, Bert Schütt, Matthias |
| author_facet | Bayer-Fluckiger, Eva van Geemen, Bert Schütt, Matthias |
| contents | We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperkähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19970 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-projective K3 surfaces with real or Salem multiplication Bayer-Fluckiger, Eva van Geemen, Bert Schütt, Matthias Algebraic Geometry Complex Variables Dynamical Systems Number Theory 11E12, 11R06, 14C30, 14D07, 14J28, 14J42, 14J50, 32G20, 37B40 We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperkähler 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. |
| title | Non-projective K3 surfaces with real or Salem multiplication |
| topic | Algebraic Geometry Complex Variables Dynamical Systems Number Theory 11E12, 11R06, 14C30, 14D07, 14J28, 14J42, 14J50, 32G20, 37B40 |
| url | https://arxiv.org/abs/2511.19970 |