Birational geometry in the study of dynamics of automorphisms and Brody/Mori/Lang hyperbolicity

Abstract

We survey our recent papers (some being joint ones) about the relation between the geometry of a compact Kähler manifold and the existence of automorphisms of positive entropy on it. We also use the language of log minimal model program (LMMP) in biraitonal geometry, but not its more sophisticated technical part. We give applications of LMMP to positivity of log canonical divisor of a Mori / Brody / Lang hyperbolic (quasi-) projective (singular) variety.

submitted to the Proceedings of the Six International Congress of Chinese Mathematicians (ICCM2013), Taipei, July 2013

References in corpus (7)

• Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy
• Dynamics of Automorphisms of Compact Complex Manifolds
• Remarks about bubbles
• Compact Kähler manifolds with automorphism groups of maximal rank
• Positivity criteria for log canonical divisors and hyperbolicity
• Tits alternative for automorphism groups of compact Kaehler manifolds
• A characterization of compact complex tori via automorphism groups