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

Abstract

This paper concerns complex algebraic K3 surfaces with an automorphism which acts trivially on the Neron-Severi group. Complementing a result by Vorontsov and Kondo, 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 mirror symmetry

19 pages, 1 figure; v3: exposition improved thanks to referee's comments

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