Invariant foliations for endomorphims of $\mathbb{P}^2$ with a pluripotentialist product structure - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

Invariant foliations for endomorphims of $\mathbb{P}^2$ with a pluripotentialist product structure

Abstract

Let $f$ be a holomorphic endomorphism of $\mathbb{P}^2$, let $T$ be its Green current and $\mu=T\wedge T$ be its equilibrium measure. We prove that if $\mu$ has a local product structure with respect to $T$ then (an iterate of) $f$ preserves a local foliation $\mathcal{F}$ on a neighborhood of $\mathrm{Supp}(T )\backslash\mathcal{E}$, where $\mathcal{E}$ denotes the exceptional set of f . If the local foliation $\mathcal{F}$ extends through $\mathcal{E}$, then it extends to $\mathbb{P}^2$ and is an invariant pencil of lines.
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Dates and versions

hal-04512333 , version 1 (20-03-2024)

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  • HAL Id : hal-04512333 , version 1

Cite

Virgile Tapiero. Invariant foliations for endomorphims of $\mathbb{P}^2$ with a pluripotentialist product structure. 2024. ⟨hal-04512333⟩
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