Global minimal models for endomorphisms of projective space

TL;DR

This paper proves the existence of global minimal models for rational endomorphisms of projective space over fields with a principal ideal domain, advancing the understanding of their algebraic structure.

Contribution

It establishes the existence of global minimal models for rational morphisms on projective space over certain fields, a new result in algebraic geometry.

Findings

Existence of global minimal models proven

Applicable to rational morphisms over fields with principal ideal domains

Advances understanding of endomorphism structures in algebraic geometry

Abstract

We prove the existence of global minimal models for rational morphisms $\phi:{\mathbb P}^N\rightarrow{\mathbb P}^N$ of projective space defined over the field of fractions of a principal ideal domain.