We will prove that there are infinitely many families of K3 surfaces which both admit a finite symplectic automorphism and are (desingularizations of) quotients of other K3 surfaces by a symplectic automorphism. These families have an unexpectedly high dimension. We apply this result to construct ``special'' isogenies between K3 surfaces which are not Galois covers between K3 surfaces but are obtained by composing cyclic Galois covers. In the case of involutions, for any $ nin mathbb{N}_{>0}$ we determine the transcendental lattices of the K3 surfaces which are $ 2^n:1$ isogenous (by the mentioned ``special'' isogeny) to other K3 surfaces.
On certain isogenies between K3 surfaces / C. Camere, A. Garbagnati. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6850. - 373:4(2020 Apr), pp. 2913-2931. [10.1090/tran/8022]
On certain isogenies between K3 surfaces
C. Camere;A. Garbagnati
2020
Abstract
We will prove that there are infinitely many families of K3 surfaces which both admit a finite symplectic automorphism and are (desingularizations of) quotients of other K3 surfaces by a symplectic automorphism. These families have an unexpectedly high dimension. We apply this result to construct ``special'' isogenies between K3 surfaces which are not Galois covers between K3 surfaces but are obtained by composing cyclic Galois covers. In the case of involutions, for any $ nin mathbb{N}_{>0}$ we determine the transcendental lattices of the K3 surfaces which are $ 2^n:1$ isogenous (by the mentioned ``special'' isogeny) to other K3 surfaces.File | Dimensione | Formato | |
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