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arxiv: math/0609686 · v3 · submitted 2006-09-25 · 🧮 math.DS · math.CV

Equidistribution towards the Green current for holomorphic maps

classification 🧮 math.DS math.CV
keywords currentgreenholomorphicpull-backanalogousassociatedclosedconverge
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Let f be a non-invertible holomorphic endomorphism of a projective space and f^n its iterate of order n. We prove that the pull-back by f^n of a generic (in the Zariski sense) hypersurface, properly normalized, converge to the Green current associated to f when n tends to infinity. We also give an analogous result for the pull-back of positive closed (1,1)-currents.

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