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 automor- phism 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.
On symplectic and non-symplectic automorphisms of K3 surfaces / A. Garbagnati, A. Sarti. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 29:1(2013 Jan), pp. 135-162. [10.4171/RMI/716]
On symplectic and non-symplectic automorphisms of K3 surfaces
A. GarbagnatiPrimo
;
2013
Abstract
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 automor- phism 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.File | Dimensione | Formato | |
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