Inverse images of positive closed currents under holomorphic endomorphisms of compact Kähler manifolds

2024/05/01 by Taeyong Ahn, Ahn, Taeyong
#math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.2405.00607

Abstract

We prove that for a surjective holomorphic endomorphism f of a compact Kähler manifold X of dimension k≥ 2 and for some integer p with 1≤ p≤ k, there exists a proper invariant analytic subset E for f such that if a positive closed (p, p)-current S can be represented by a smooth form in a neighborhood of E, the sequence d_p^-n(fⁿ)^*(S-α_S) converges to 0 exponentially fast in the sense of currents, where d_p is the dynamical degree of order p and α_S is a smooth closed (p, p)-form in the de Rham cohomology class of S.

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• Equidistribution towards the Green current for holomorphic maps
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