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Brolin's Theorem for curves in two complex dimensions

Charles Favre·Mattias Jonsson
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Abstract

Given a holomorphic selfmap f of the complex projective plane of algebraic degree at least 2, we give sufficient conditions on a positive closed (1,1) current S of unit mass under which the normalized pullbacks of S under iterates of f converge to the Green current T. In particular, we completely characterize the plane algebraic curves whose normalized pullbacks converge weakly to T.

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Charles Favre, Mattias Jonsson. 2001-05-31. Brolin's Theorem for curves in two complex dimensions. https://arxiv.org/abs/math/0105260

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