Article contents
Complex multiplication and Noether–Lefschetz loci of the twistor space of a K3 surface
Published online by Cambridge University Press: 27 July 2023
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.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 176 , Issue 1 , January 2024 , pp. 17 - 38
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
References
- 1
- Cited by