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Pré-Publication, Document De Travail Année : 2017

An application of $p$-adic integration to the dynamics of a birational transformation preserving a fibration

Résumé

Let $f\colon X \dashrightarrow X$ be a birational transformation of a projective manifold $X$ whose Kodaira dimension $\kappa(X)$ is non-negative. We show that, if there exist a meromorphic fibration $\pi \colon X\dashrightarrow B$ and a pseudo-automorphism $f_B\colon B\dashrightarrow B$ which preserves a big line bundle $L\in Pic(B)$ and such that $f_B\circ \pi=\pi\circ f$, then $f_B$ has finite order. As a corollary we show that, for projective irreducible symplectic manifolds of type $K3^{[n]}$ or generalized Kummer, the first dynamical degree characterizes the birational transformations admitting a Zariski-dense orbit.

Dates et versions

hal-01579234 , version 1 (30-08-2017)

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Federico Lo Bianco. An application of $p$-adic integration to the dynamics of a birational transformation preserving a fibration. 2017. ⟨hal-01579234⟩
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