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- Title
Complex multiplication and Noether–Lefschetz loci of the twistor space of a K3 surface.
- Authors
VIGANÒ, FRANCESCO
- Abstract
For an algebraic K3 surface with complex multiplication (CM), algebraic fibres of the associated twistor space away from the equator are again of CM type. In this paper, we show that algebraic fibres corresponding to points at the same altitude of the twistor base ${S^2} \simeq \mathbb{P}_\mathbb{C}^1$ share the same CM endomorphism field. Moreover, we determine all the admissible Picard numbers of the twistor fibres.
- Subjects
PICARD number; ENDOMORPHISMS; ALGEBRAIC surfaces; MULTIPLICATION; LOCUS (Mathematics); FIBERS
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2024, Vol 176, Issue 1, p17
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004123000336