Complex Multiplication and Noether-Lefschetz Loci of the Twistor Space of a K3 Surface

2021/02/15 by Viganò, Francesco
#14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.07285

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 S²≃ ℙ¹_ℂ share the same CM endomorphism field. Moreover, we determine all the admissible Picard numbers of the twistor fibres.

Related

• Complex multiplication in twistor spaces
• Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci
• Geometry of some twistor spaces of algebraic dimension one
• Twistor spaces for supersingular K3 surfaces
• Explicit families of K3 surfaces having real multiplication