Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties

2019/02/16 by Yohsuke Matsuzawa, Matsuzawa, Yohsuke · 1 citation
Mathematics · #14E30 #37P55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1902.06072

openalex publication_date 2019/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Kawaguchi-Silverman conjecture (KSC) and Shibata's conjecture on ample canonical heights for endomorphisms on several classes of algebraic varieties including varieties of Fano type and projective toric varieties. We also prove KSC for group endomorphisms of linear algebraic groups. We also propose a possible approach to the conjecture using equivariant MMP.

Citations

• (Relative) dynamical degrees of rational maps over an algebraic closed field
• On upper bounds of arithmetic degrees
• The canonical heights for Jordan blocks of small eigenvalues, preperiodic points, and the arithmetic degrees

Cited by

• Dynamics of Projectivized Toric Vector Bundles

Related

• A note on Kawaguchi-Silverman conjecture
• Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism
• Canonical heights on hyper-K "ahler varieties and the\n Kawaguchi-Silverman conjecture
• Endomorphisms of a variety of Ueno type and Kawaguchi-Silverman Conjecture
• Ample canonical heights for endomorphisms on projective varieties