ON THE DYNAMICAL DEGREES OF MEROMORPHIC MAPS PRESERVING A FIBRATION

By T. Dinh, Viet Anh Nguyen, Tuyen T. T. Truong. 2011

55 citations recorded by the source corpus.

Let f be a dominant meromorphic self-map on a compact Kahler manifold X which preserves a meromorphic fibration π : X → Y of X over a compact Kahler 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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b39a7859ac33cf241e1b39509384f10524beee17

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Equidistribution problems of complex dynamics in higher dimension (2016, background): “Specific needs can be obtained by going through the details of the proof of the above theorem, see [13, 22, 26].”
Degrees of iterates of rational maps on normal projective varieties (2017, methodology): “Moreover, following closely the method of [31], one can also obtain another proof of the product formula due to Dinh–Nguyen–Truong [9].”
Relative dynamical degrees of correspondences over a field of arbitrary characteristic (2016, methodology): “3 in [9] (see also [10]) was proven, in the case f is a dominant rational map, by using the following (which is in lines 2-3 in the proof of that lemma): (fn)∗(π∗(ω Y )∧ω q X) ≤ (fn)∗(π∗(ω Y )) o ∧ (fn)∗(ω X).”