On symplectic and non--symplectic automorphisms of K3 surfaces

Details On symplectic and non--symplectic automorphisms of K3 surfaces On symplectic and non--symplectic automorphisms of K3 surfaces

2010-06-08

arxiv.org/abs/1006.1604v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

In this paper we investigate when the generic member of a family of K3 surfaces admitting a non--symplectic automorphism of finite order admits also a symplectic automorphism of the same order. We give a complete answer to this question if the order of the automorphism is a prime number and we provide several examples and partial results otherwise. Moreover we prove that, under certain conditions, a K3 surface admitting a non--symplectic automorphism of prime odd order, $p$, also admits a non--symplectic automorphism of order $2p$. This generalizes a previous result by J. Dillies for $p=3$.

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