THE g-PERIODIC SUBVARIETIES FOR AN AUTOMORPHISM g OF POSITIVE ENTROPY ON A COMPACT KÄHLER MANIFOLD
نویسنده
چکیده
For a compact Kähler manifold X and a strongly primitive automorphism g of positive entropy, it is shown that X has at most ρ(X) of g-periodic prime divisors. When X is a projective threefold, every prime divisor containing infinitely many g-periodic curves, is shown to be g-periodic (a result in the spirit of the Dynamic Manin-Mumford conjecture as in [17]).
منابع مشابه
Solvable automorphism groups of a compact Kähler manifold
Let X be a compact Kähler manifold of complex dimension n, and let G be a connected solvable subgroup of the automorphism group Aut(X). Let N(G) be the normal subgroup of G of elements of null entropy. The aim of this short paper is to show that if X admits a Kähler metric invariant under G then G/N(G) is a free abelian group of rank ≤ n − 1 and that the rank estimate is optimal. This proves af...
متن کاملSolvable automorphisms groups of a compact Kähler manifold
Let X be a compact Kähler manifold of complex dimension n, and let G be a connected solvable subgroup of the automorphism group Aut(X). Let N(G) be the normal subgroup of G of elements of null entropy. The aim of this short paper is to show that G/N(G) is a free abelian group of rank ≤ n− 1 and that the rank estimate is optimal. This proves the conjecture of Tits type in [6] affirmatively. The ...
متن کاملON LOCAL HUDETZ g-ENTROPY
In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.
متن کاملNILPOTENCY AND SOLUBILITY OF GROUPS RELATIVE TO AN AUTOMORPHISM
In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...
متن کاملCompact Lie Group Actions on Closed Manifolds of Non-positive Curvature
A. Borel proved that, if a finite group F acts effectively and continuously on a closed aspherical manifold M with centerless fundamental group π1(M), then a natural homomorphism ψ from F to the outer automorphism group Outπ1(M) of π1(M), called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel’s theorem holds for a compact Lie group G acting ...
متن کامل