Commentarii Mathematici Helvetici


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Volume 86, Issue 4, 2011, pp. 817–840
DOI: 10.4171/CMH/241

Published online: 2011-09-22

Comparison of dynamical degrees for semi-conjugate meromorphic maps

Tien-Cuong Dinh[1] and Viêt-Anh Nguyên[2]

(1) Institut Mathématique de Jussieu, Paris, France
(2) Université Paris-Sud 11, Orsay, France

Let $f\colon X\rightarrow X$ be a dominant meromorphic map on a projective manifold $X$ which preserves a meromorphic fibration $\pi\colon X\rightarrow Y$ of $X$ over a projective manifold $Y$. We establish formulas relating the dynamical degrees of $f$, the dynamical degrees of $f$ relative to the fibration and the dynamical degrees of the map $g\colon Y\rightarrow Y$ induced by $f$. Applications are given.

Keywords: Semi-conjugate maps, dynamical degree, relative dynamical degree

Dinh Tien-Cuong, Nguyên Viêt-Anh: Comparison of dynamical degrees for semi-conjugate meromorphic maps. Comment. Math. Helv. 86 (2011), 817-840. doi: 10.4171/CMH/241