A geometric proof of the Lelong-Poincaré formula - Université de Lorraine
Journal Articles Proyecciones : Revista de Matemática Year : 2013

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.

Dates and versions

hal-01867411 , version 1 (04-09-2018)

Identifiers

Cite

A El Amrani, A Jeddi. A geometric proof of the Lelong-Poincaré formula. Proyecciones : Revista de Matemática, 2013, 32 (1), pp.1 - 13. ⟨10.4067/S0716-09172013000100001⟩. ⟨hal-01867411⟩
110 View
0 Download

Altmetric

Share

More