Multiplicity of holomorphic functions

Charles Favre

doi:10.1007/s002080050016

Multiplicity of holomorphic functions

Charles Favre

KTH Royal Institute of Technology
Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

The main result of this paper concerns an analytic version of Birkhoff's ergodic theorem. It allows us to define asymptotic multiplicities given any algebraically stable rational map f : ℙ² → ℙ². This is the key for our study of the singularities of the Green current T associated to f. We characterize the points where the Lelong number of T is strictly positive.

Original language	English
Pages (from-to)	355-378
Number of pages	24
Journal	Mathematische Annalen
Volume	316
Issue number	2
DOIs	https://doi.org/10.1007/s002080050016
Publication status	Published - 1 Jan 2000
Externally published	Yes

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10.1007/s002080050016

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abstract = "The main result of this paper concerns an analytic version of Birkhoff's ergodic theorem. It allows us to define asymptotic multiplicities given any algebraically stable rational map f : ℙ2 → ℙ2. This is the key for our study of the singularities of the Green current T associated to f. We characterize the points where the Lelong number of T is strictly positive.",

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AB - The main result of this paper concerns an analytic version of Birkhoff's ergodic theorem. It allows us to define asymptotic multiplicities given any algebraically stable rational map f : ℙ2 → ℙ2. This is the key for our study of the singularities of the Green current T associated to f. We characterize the points where the Lelong number of T is strictly positive.

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DO - 10.1007/s002080050016

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JO - Mathematische Annalen

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Multiplicity of holomorphic functions

Abstract

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