2024/08/01 by Sheng Meng, Guolei Zhong, Meng, Sheng +1 · 2 citations
Computer Science · Mathematics · #14E30 #14H30 #14M25 #20K30 #32H50 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2408.00566
openalex publication_date 2024/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a ℚ-factorial klt projective variety admitting an int-amplified endomorphism f, i.e., the modulus of any eigenvalue of f^*|NS(X) is greater than 1. We prove Kawaguchi-Silverman conjecture for f and also any other surjective endomorphism of X: the first dynamical degree equals the arithmetic degree of any point with Zariski dense orbit. This generalizes an early result of Kawaguchi and Silverman for the polarized f case, i.e., f^*|NS(X) is diagonalizable with all eigenvalues of the same modulus greater than 1.