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Multiplicity of holomorphic functions

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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 \(f : \mathbb{P}^2 \to \mathbb{P}^2\). 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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Received: 30 July 1999

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Favre, C. Multiplicity of holomorphic functions. Math Ann 316, 355–378 (2000). https://doi.org/10.1007/s002080050016

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  • DOI: https://doi.org/10.1007/s002080050016

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