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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On certain isogenies between K3 surfaces


Authors: Chiara Camere and Alice Garbagnati
Journal: Trans. Amer. Math. Soc. 373 (2020), 2913-2931
MSC (2010): Primary 14J28, 14J50; Secondary 14J10
DOI: https://doi.org/10.1090/tran/8022
Published electronically: January 28, 2020
MathSciNet review: 4069236
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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 $n\in \mathbb {N}_{>0}$ we determine the transcendental lattices of the K3 surfaces which are $2^n:1$ isogenous (by the mentioned “special” isogeny) to other K3 surfaces.


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Additional Information

Chiara Camere
Affiliation: Università degli Studi di Milano, Dipartimento di Matematica, via Cesare Saldini 50, 20133 Milano, Italy
Email: chiara.camere@unimi.it

Alice Garbagnati
Affiliation: Università degli Studi di Milano, Dipartimento di Matematica, via Cesare Saldini 50, 20133 Milano, Italy
MR Author ID: 826065
Email: alice.garbagnati@unimi.it

Keywords: K3 surfaces, quotients, symplectic automorphisms on K3 surfaces, Galois covers between K3 surfaces, isogenies between K3 surfaces
Received by editor(s): June 5, 2019
Received by editor(s) in revised form: July 22, 2019, and September 18, 2019
Published electronically: January 28, 2020
Article copyright: © Copyright 2020 American Mathematical Society