Equidistribution of Inverse Images of Positive Closed Currents

2025
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Author: Taeyong Ahn
Published in: Complex Geometric Analysis
Publisher: Springer Nature Singapore

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Abstract

The chapter begins by revisiting Brolin's seminal theorem on the equidistribution of inverse images of points under polynomial iteration, setting the stage for a deeper exploration into higher-dimensional generalizations. It introduces key conjectures by Dinh and Sibony, which aim to extend Brolin's results to holomorphic endomorphisms on complex projective spaces. The text delves into the dynamics of these endomorphisms, focusing on the behavior of Green currents and their convergence properties. A significant portion of the chapter is dedicated to the intermediate bidegree cases, where the introduction of superpotentials by Dinh and Sibony has resolved major obstacles. The chapter also considers the extension of these results to compact Kähler manifolds, discussing the challenges and potential generalizations. It concludes with open questions that push the boundaries of current understanding, inviting further research and exploration in this intricate field.

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Metadata
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Title: Equidistribution of Inverse Images of Positive Closed Currents
Author: Taeyong Ahn
Publisher: Springer Nature Singapore
Book: Complex Geometric Analysis
Print ISBN: 978-981-9604-46-3

Electronic ISBN: 978-981-9604-47-0

Copyright Year: 2025
DOI: https://doi.org/10.1007/978-981-96-0447-0_1

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