The modularity of K3 surfaces with non-symplectic group actions

Autor:	Livné, Ron, Schuett, Matthias, Yui, Noriko
Rok vydání:	2009
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory 14J32 14J28 14J27 14J20 14G10 11G40 11F80
Druh dokumentu:	Working Paper
Popis:	We consider complex K3 surfaces with a non-symplectic group acting trivially on the algebraic cycles. Vorontsov and Kondo classified those K3 surfaces with transcendental lattice of minimal rank. The purpose of this note is to study the Galois representations associated to these K3 surfaces. The rank of the transcendental lattices is even and varies from 2 to 20, excluding 8 and 14. We show that these K3 surfaces are dominated by Fermat surfaces, and hence they are all of CM type. We will establish the modularity of the Galois representations associated to them. Also we discuss mirror symmetry for these K3 surfaces in the sense of Dolgachev, and show that a mirror K3 surface exists with one exception. Comment: 20 pages, 7 tables; v2: minor changes; to appear in math. ann
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0904.1922 Zobrazit plný text záznamu View this record from Arxiv