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

2022/11/24 by François Berteloot, Berteloot, François, Maxence Brévard +1
Mathematics · Physics and Astronomy · #32H50 #32U40 #37F44 #37F80 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2211.13636

openalex publication_date 2022/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the context of holomorphic families of endomorphisms of \mathbb P^k, we prove that stability in the sense of [BBD18] 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 [BBD18] and better relate stability to post-critical normality.

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