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- W2995963898 abstract "We establish the Geometric Dynamical Northcott Property for polarized endomorphisms of a projective normal variety over a function field $mathbf{K}$ of characteristic zero. This extends previous results of Benedetto, Baker and DeMarco in dimension $1$, and of Chatzidakis-Hrushovski in higher dimension. Our proof uses complex dynamics arguments and does not rely on the previous one. We first show that when $mathbf{K}$ is the field of rational functions of a smooth complex projective variety, the canonical height of a subvariety is the mass of the appropriate bifurcation current and that a marked point is stable if and only if its canonical height is zero. We then establish the Geometric Dynamical Northcott Property using a similarity argument. Moving from points to subvarieties, we propose, for polarized endomorphisms, a dynamical version of the Geometric Bogomolov Conjecture, recently proved by Cantat, Gao, Habegger and Xie. We establish several cases of this conjecture notably non-isotrivial polynomial skew-product with an isotrivial first coordinate." @default.
- W2995963898 created "2019-12-26" @default.
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- W2995963898 date "2019-12-17" @default.
- W2995963898 modified "2023-09-27" @default.
- W2995963898 title "The Geometric Dynamical Northcott and Bogomolov Properties" @default.
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