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Complex multiplication and Noether–Lefschetz loci of the twistor space of a K3 surface.
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Jan2024, Vol. 176 Issue 1, p17-38. 22p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 176
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 174324269
- Full Text :
- https://doi.org/10.1017/S0305004123000336