On the dynamical degrees of meromorphic maps preserving a fibration

Tien-Cuong Dinh, Viet-Anh Nguyen, and Tuyen Trung Truong

Abstract: Let f be a dominant meromorphic self-map on a compact Kähler manifold X which preserves a meromorphic fibration π : X → Y of X over a compact Kähler manifold Y. We compute the dynamical degrees of f in terms of its dynamical degrees relative to the fibration and the dynamical degrees of the map g : Y → Y induced by f. We derive from this result new properties of some fibrations intrinsically associated to X when this manifold admits an interesting dynamical system.

Journal: Commun. Contemp. Math. 14 (2012), 1250042.

DOI: 10.1142/S0219199712500423