TY - JOUR

T1 - K3 surfaces with non-symplectic automorphisms of 2-power order

AU - Schütt, Matthias

N1 - Funding information: The author would like to thank S. Kondo¯ for stimulating discussions and the referee for many helpful comments. Funding from DFG under research grant Schu 2266/2-2 is gratefully acknowledged.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - This paper concerns complex algebraic K3 surfaces with an automorphism which acts trivially on the Néron-Severi group. Complementing a result by Vorontsov and Kondō, we determine those K3 surfaces where the order of the automorphism is a 2-power and equals the rank of the transcendental lattice. We also study the arithmetic of these K3 surfaces and comment on relations with mirror symmetry.

AB - This paper concerns complex algebraic K3 surfaces with an automorphism which acts trivially on the Néron-Severi group. Complementing a result by Vorontsov and Kondō, we determine those K3 surfaces where the order of the automorphism is a 2-power and equals the rank of the transcendental lattice. We also study the arithmetic of these K3 surfaces and comment on relations with mirror symmetry.

KW - 2-elementary lattice

KW - Delsarte surface

KW - Elliptic surface

KW - K3 surface

KW - Mirror symmetry

KW - Non-symplectic automorphism

UR - http://www.scopus.com/inward/record.url?scp=70449130636&partnerID=8YFLogxK

UR - https://arxiv.org/abs/0807.3708

U2 - 10.1016/j.jalgebra.2009.06.021

DO - 10.1016/j.jalgebra.2009.06.021

M3 - Article

AN - SCOPUS:70449130636

VL - 323

SP - 206

EP - 223

JO - Journal of algebra

JF - Journal of algebra

SN - 0021-8693

IS - 1

ER -