Revista Matemática Iberoamericana
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Published online: 2013-01-14
On symplectic and non-symplectic automorphisms of K3 surfacesAlice Garbagnati and Alessandra Sarti (1) Università degli Studi di Milano, Italy
(2) Université de Poitiers, Futuroscope Chasseneuil, France
In this paper we investigate when the generic member of a family of complex 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 $p=3$.
Keywords: K3 surfaces, automorphisms
Garbagnati Alice, Sarti Alessandra: On symplectic and non-symplectic automorphisms of K3 surfaces. Rev. Mat. Iberoam. 29 (2013), 135-162. doi: 10.4171/RMI/716