Automorphism groups of positive entropy on minimal projective varieties
De-Qi Zhang

TL;DR
This paper characterizes the structure of minimal projective varieties with automorphisms of positive entropy and provides bounds on their dynamical degrees, extending to higher dimensions.
Contribution
It generalizes the understanding of automorphism groups with positive entropy on minimal varieties and establishes effective bounds for their dynamical degrees.
Findings
Structural description of minimal projective threefolds with such automorphisms
Extension of results to higher-dimensional smooth minimal pairs
Effective lower bounds for the first dynamical degree in boundary cases
Abstract
We determine the geometric structure of a minimal projective threefold having two `independent and commutative' automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X, G). As a consequence, we give an effective lower bound for the first dynamical degree of these automorphisms of X fitting the `boundary case'.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry
