An upper bound for the height for regular affine automorphisms of Aⁿ

2009/09/16 by ChongGyu Lee, Lee, ChongGyu · 1 citation
Mathematics · #11G50 #32H50 #37P05 #37P30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0909.3107

openalex publication_date 2009/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2006, Kawaguchi proved a lower bound for height of h(f(P)) when f is a regular affine automorphism of A², and he conjectured that a similar estimate is also true for regular affine automorphisms of Aⁿ for n>2. In this paper we prove Kawaguchi's conjecture. This implies that Kawaguchi's theory of canonical heights for regular affine automorphisms of projective space is true in all dimensions.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Cited by

• Local and global canonical height functions for affine space regular automorphisms

Related

• Local and global canonical height functions for affine space regular automorphisms
• Canonical height functions on the affine plane associated with polynomial automorphisms
• Canonical heights on hyper-K "ahler varieties and the\n Kawaguchi-Silverman conjecture
• The height of the automorphism tower of a group
• Variation of the canonical height for polynomials in several variables