Details
| Original language | English |
|---|---|
| Pages (from-to) | 333-355 |
| Number of pages | 23 |
| Journal | Mathematische Annalen |
| Volume | 348 |
| Issue number | 2 |
| Publication status | Published - 2010 |
Abstract
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In: Mathematische Annalen, Vol. 348, No. 2, 2010, p. 333-355.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The modularity of K3 surfaces with non-symplectic group actions
AU - Livné, Ron
AU - Schütt, Matthias
AU - Yui, Noriko
N1 - Funding information: R. Livné was partially supported by an ISF grant. M. Schütt was supported by Deutsche Forschungsgemeinschaft (DFG) under grant Schu 2266/2-2. N. Yui was supported in part by Discovery Grant of the Natural Sciences and Engineering Research Council (NSERC) of Canada.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77954955540&partnerID=8YFLogxK
UR - https://arxiv.org/abs/0904.1922
U2 - 10.1007/s00208-009-0475-9
DO - 10.1007/s00208-009-0475-9
M3 - Article
AN - SCOPUS:77954955540
VL - 348
SP - 333
EP - 355
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 2
ER -