A geometric proof of the Lelong-Poincaré formula

Abstract : We propose a geometric proof of the fundamental Lelong-Poincaré formula : ddc log |/ | = [/ = 0] where f is any nonzero holomorphic function defined on a complex analytic manifold V and [/ = 0] is the integration current on the divisor of the zeroes of /. Our approach is based, via the local parametrization theorem, on a precise study of the local geometry of the hypersurface given by /. Our proof extends naturally to the meromorphic case.
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A El Amrani, A Jeddi. A geometric proof of the Lelong-Poincaré formula. Proyecciones : Revista de Matemática, Universidad Católica del Norte, 2013, 32 (1), pp.1 - 13. ⟨10.4067/S0716-09172013000100001⟩. ⟨hal-01867411⟩

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