On the Kawaguchi--Silverman Conjecture for birational automorphisms of irregular varieties

2022/04/21 by Jungkai-Alfred Chen, Hsueh-Yung Lin, Chen, Jungkai Alfred +3
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2204.09845

openalex publication_date 2022/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the main open parts of the Kawaguchi--Silverman Conjecture, asserting that for a birational self-map f of a smooth projective variety X defined over \mathbb Q, the arithmetic degree α_f(x) exists and coincides with the first dynamical degree δ_f for any \mathbb Q-point x of X with a Zariski dense orbit. Among other results, we show that this holds when X has Kodaira dimension zero and irregularity q(X) ≥ dim X -1 or X is an irregular threefold (modulo one possible exception). We also study the existence of Zariski dense orbits, with explicit examples.

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