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

Autor:	Viganò, Francesco
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry 14J28
Druh dokumentu:	Working Paper
Popis:	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 $S^2\simeq \mathbb{P}^1_\mathbb{C}$ share the same CM endomorphism field. Moreover, we determine all the admissible Picard numbers of the twistor fibres. Comment: 24 pages, 8 different figures (one of which repeating 4 times, one of which repeating 2 times)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.07285 Zobrazit plný text záznamu View this record from Arxiv