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Ramification current, post-critical normality and stability of holomorphic endomorphisms of $\mathbb P^k$

Volume 263 / 2023

François Berteloot, Maxence Brévard Fundamenta Mathematicae 263 (2023), 253-270 MSC: Primary 37F44; Secondary 37F80, 32H50, 32U40. DOI: 10.4064/fm279-6-2023 Published online: 5 October 2023

Abstract

In the context of holomorphic families of endomorphisms of $\mathbb P^k$, we prove that stability in the sense of [F. Berteloot et al., Ann. Sci. École Norm. Sup. 51 (2018)] is equivalent to a summability condition for the post-critical mass and to the convergence of a suitably defined ramification current. This allows us to both simplify the approach of the above-mentioned paper and better relate stability to post-critical normality.

Authors

  • François BertelootInstitut de Mathématiques de Toulouse
    Université Paul Sabatier
    F-31062 Toulouse Cedex 9, France
    e-mail
  • Maxence BrévardInstitut de Mathématiques de Toulouse
    Université Paul Sabatier
    F-31062 Toulouse Cedex 9, France
    e-mail

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