The modularity of K3 surfaces with non-symplectic group actions

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  • Hebrew University of Jerusalem (HUJI)
  • Queen's University Kingston
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OriginalspracheEnglisch
Seiten (von - bis)333-355
Seitenumfang23
FachzeitschriftMathematische Annalen
Jahrgang348
Ausgabenummer2
PublikationsstatusVeröffentlicht - 2010

Abstract

We consider complex K3 surfaces with a non-symplectic group acting trivially on the algebraic cycles. Vorontsov and Kondō 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.

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The modularity of K3 surfaces with non-symplectic group actions. / Livné, Ron; Schütt, Matthias; Yui, Noriko.
in: Mathematische Annalen, Jahrgang 348, Nr. 2, 2010, S. 333-355.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Livné R, Schütt M, Yui N. The modularity of K3 surfaces with non-symplectic group actions. Mathematische Annalen. 2010;348(2):333-355. doi: 10.1007/s00208-009-0475-9
Livné, Ron ; Schütt, Matthias ; Yui, Noriko. / The modularity of K3 surfaces with non-symplectic group actions. in: Mathematische Annalen. 2010 ; Jahrgang 348, Nr. 2. S. 333-355.
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AU - Schütt, Matthias

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