Some aspects of explicit birational geometry inspired by complex dynamics

TL;DR

This paper explores how concepts from complex dynamics, like topological entropy and dynamical degrees, can be applied to study birational and biregular selfmaps of projective and Kähler manifolds, using concrete examples.

Contribution

It demonstrates the effective application of dynamical and minimal model theory ideas to explicit problems in birational geometry.

Findings

Illustrates the use of topological entropy and dynamical degrees in birational geometry

Provides concrete examples connecting complex dynamics with minimal model theory

Advances understanding of selfmaps on projective and Kähler manifolds

Abstract

Our aim is to illustrate how one can effectively apply the basic ideas and notions of topological entropy and dynamical degrees, together with recent progress of minimal model theory in higher dimension, for an explicit study of birational or biregular selfmaps of projective or compact K\"ahler manifolds, through concrete examples.