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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On certain isogenies between K3 surfaces
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by Chiara Camere and Alice Garbagnati PDF
Trans. Amer. Math. Soc. 373 (2020), 2913-2931 Request permission

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
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 2913-2931
  • MSC (2010): Primary 14J28, 14J50; Secondary 14J10
  • DOI: https://doi.org/10.1090/tran/8022
  • MathSciNet review: 4069236