K3 surfaces with Picard number 2, Salem polynomials and Pell equation
Kenji Hashimoto, JongHae Keum, and Kwangwoo Lee
TL;DR
This paper classifies all Salem polynomials associated with automorphisms of projective K3 surfaces with Picard number 2 by linking them to solutions of the Pell equation, providing a complete characterization.
Contribution
It explicitly determines all Salem polynomials for automorphisms of such K3 surfaces through Pell equation solutions, a novel classification result.
Findings
All Salem polynomials for these automorphisms are characterized.
Automorphisms correspond to solutions of Pell equations.
Complete classification of automorphisms with infinite order.
Abstract
If an automorphism of a projective K3 surface with Picard number 2 is of infinite order, then the automorphism corresponds to a solution of Pell equation. In this paper, by solving this equation, we determine all Salem polynomials of symplectic and anti-symplectic automorphisms of projective K3 surfaces with Picard number 2.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions