Revista Matemática Iberoamericana


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Volume 29, Issue 1, 2013, pp. 135–162
DOI: 10.4171/RMI/716

Published online: 2013-01-14

On symplectic and non-symplectic automorphisms of K3 surfaces

Alice Garbagnati[1] and Alessandra Sarti[2]

(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. Iberoamericana 29 (2013), 135-162. doi: 10.4171/RMI/716