An equidistribution theorem for biraitonal maps of ℙ^k

2020/09/19 by Taeyong Ahn, Ahn, Taeyong
Mathematics · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2009.09203

openalex publication_date 2020/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an equidistribution theorem of positive closed currents for a certain class of birational maps f₊:ℙ^k→ℙ^k of algebraic degree d≥ 2 satisfying \bigcup_{n≥ 0}f_-ⁿ(I⁺)∩ \bigcup_{n≥ 0}f₊ⁿ(I^-)=∅, where f_- is the inverse of f₊ and I^± are the sets of indeterminacy for f_±, respectively.

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