Height estimates for dominant endomorphisms on projective varieties

TL;DR

This paper generalizes the concept of height estimates for polarizable endomorphisms to arbitrary dominant endomorphisms on projective varieties by introducing height expansion and contraction coefficients.

Contribution

It introduces height expansion and contraction coefficients to extend height estimates from polarizable to arbitrary dominant endomorphisms.

Findings

Defined height expansion and contraction coefficients.

Extended height estimate framework to all dominant endomorphisms.

Provided theoretical foundation for future research in height dynamics.

Abstract

A polarizable endomorphism on a projective variety enables us to consider given morphism as constant multiplication in the height function. In this paper, we will generalize it for arbitrary dominant endomorphism by defining the height expansion and contraction coefficients.