Explicit canonical heights for divisors relative to endomorphisms of $\mathbb{P}^N$

TL;DR

This paper provides explicit bounds on the difference between naive and canonical heights of divisors in projective space relative to a given endomorphism, aiding in understanding height functions in algebraic dynamics.

Contribution

It introduces explicit bounds for height differences of divisors under endomorphisms of projective space, advancing computational tools in algebraic dynamics.

Findings

Explicit bounds on height differences are established.

Results apply to divisors in projective space under endomorphisms.

Enhances understanding of height functions in algebraic geometry.

Abstract

Given an endomorphism f of projective space, we exhibit explicit bounds on the difference between the naive height of a divisor and its canonical height relative to f.