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

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Cited by in corpus (14)

• On entropy for autoequivalences of the derived category of curves
• Categorical polynomial entropy
• On the categorical entropy and the topological entropy
• Extremal rays and automorphisms of holomorphic symplectic varieties
• Finiteness properties of pseudo-hyperbolic varieties
• Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces
• Compact Kähler threefolds with the action of an abelian group of maximal rank
• On entropy of spherical twists
• Algebraic entropy for smooth projective varieties
• Higher arithmetic degrees of dominant rational self-maps
• n-Dimensional Projective Varieties with the Action of an Abelian Group of Rank n-1
• Primitive automorphisms of a simple abelian variety
• Non-liftability of automorphism groups of a K3 surface in positive characteristic
• Geometric methods in holomorphic dynamics