Complex multiplication in twistor spaces
Algebraic Geometry
2020-03-12 v2
Abstract
Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarized K3 surface with complex multiplication, all algebraic fibres of its twistor space away from the equator have complex multiplication as well.
Keywords
Cite
@article{arxiv.1910.13788,
title = {Complex multiplication in twistor spaces},
author = {Daniel Huybrechts},
journal= {arXiv preprint arXiv:1910.13788},
year = {2020}
}
Comments
21 pages. Revision takes into account various insightful comments of two anonymous referees. In particular the equation of the CM extension for the twistor fibre (Corollary 3.10) has been corrected and from Section 3.2 the assumption (\ell'.\ell')>0 has been added. To appear in IMRN