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. - (2020). [Epub ahead of print]
Titolo: | On certain isogenies between K3 surfaces | |
Autori: | ||
Parole Chiave: | K3 surfaces; Quotients; Symplectic automorphisms on K3 surfaces; Galois covers between K3 surfaces; Isogenies between K3 surfaces | |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria | |
Data di pubblicazione: | 2020 | |
Rivista: | ||
Tipologia: | Article (author) | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1090/tran/8022 | |
Appare nelle tipologie: | 01 - Articolo su periodico |
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relatedK3-final.pdf | Post-print, accepted manuscript ecc. (versione accettata dall'editore) | Open Access Visualizza/Apri | ||
1905.08859.pdf | Pre-print (manoscritto inviato all'editore) | Open Access Visualizza/Apri | ||
S0002-9947-2020-08022-2.pdf | Publisher's version/PDF | Administrator Richiedi una copia |