Some aspects of explicit birational geometry inspired by complex dynamics

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 Kähler manifolds, through concrete examples.

A survey article for ICM2014 proceedings (Invited talk at Section 4). Format, typos, references, ambiguities are corrected

References in corpus (2)

• Automorphism groups of Calabi-Yau manifolds of Picard number two
• Tits alternative in hypekähler manifolds

Cited by in corpus (6)

• Extremal rays and automorphisms of holomorphic symplectic varieties
• Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces
• On entropy of spherical twists
• Higher arithmetic degrees of dominant rational self-maps
• Non-liftability of automorphism groups of a K3 surface in positive characteristic
• Primitive automorphisms of a simple abelian variety