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Online ISSN 1534-7486; Print ISSN 1056-3911
Equations for a K3 Lehmer map
Authors:
Simon Brandhorst and Noam D. Elkies
Journal:
J. Algebraic Geom. 32 (2023), 641-675
DOI:
https://doi.org/10.1090/jag/810
Published electronically:
April 26, 2023
Full-text PDF
Abstract | References | Additional Information
Abstract: C. T. McMullen proved the existence of a K3 surface with an automorphism of entropy given by the logarithm of Lehmer’s number, which is the minimum possible among automorphisms of complex surfaces. We reconstruct equations for the surface and its automorphism from the Hodge theoretic model provided by McMullen. The approach is computer aided and relies on finite non-symplectic automorphisms, $p$-adic lifting, elliptic fibrations and the Kneser neighbor method for $\mathbb {Z}$-lattices. It can be applied to reconstruct any automorphism of an elliptic K3 surface from its action on the Neron-Severi lattice.
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Additional Information
Simon Brandhorst
Affiliation:
Fakultät für Mathematik und Informatik, Universität des Saarlandes, Campus E2.4, 66123 Saarbrücken, Germany
MR Author ID:
1070371
ORCID:
0000-0002-0249-9971
Email:
brandhorst@math.uni-sb.de
Noam D. Elkies
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
MR Author ID:
229330
Email:
elkies@math.harvard.edu
Received by editor(s):
March 21, 2021
Received by editor(s) in revised form:
June 8, 2021
Published electronically:
April 26, 2023
Additional Notes:
The first author: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) – Projektnummer 286237555 – TRR 195 [was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 286237555 – TRR 195].
Article copyright:
© Copyright 2023
University Press, Inc.