A geometric proof of the Lelong-Poincaré formula

We propose a geometric proof of the fundamental Lelong-Poincaré formula : dd c 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 parame...

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Autores principales:	El Amrani,M, Jeddi,A
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2013
Materias:	Complex analytic manifolds analytic sets local parametrization theorem integration currents branching coverings
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100001
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spelling	oai:scielo:S0716-091720130001000012014-09-09A geometric proof of the Lelong-Poincaré formulaEl Amrani,MJeddi,A Complex analytic manifolds analytic sets local parametrization theorem integration currents branching coverings We propose a geometric proof of the fundamental Lelong-Poincaré formula : dd c 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.32 n.1 20132013-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100001en10.4067/S0716-09172013000100001
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Complex analytic manifolds analytic sets local parametrization theorem integration currents branching coverings
spellingShingle	Complex analytic manifolds analytic sets local parametrization theorem integration currents branching coverings El Amrani,M Jeddi,A A geometric proof of the Lelong-Poincaré formula
description	We propose a geometric proof of the fundamental Lelong-Poincaré formula : dd c 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.
author	El Amrani,M Jeddi,A
author_facet	El Amrani,M Jeddi,A
author_sort	El Amrani,M
title	A geometric proof of the Lelong-Poincaré formula
title_short	A geometric proof of the Lelong-Poincaré formula
title_full	A geometric proof of the Lelong-Poincaré formula
title_fullStr	A geometric proof of the Lelong-Poincaré formula
title_full_unstemmed	A geometric proof of the Lelong-Poincaré formula
title_sort	geometric proof of the lelong-poincaré formula
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2013
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100001
work_keys_str_mv	AT elamranim ageometricproofofthelelongpoincareformula AT jeddia ageometricproofofthelelongpoincareformula AT elamranim geometricproofofthelelongpoincareformula AT jeddia geometricproofofthelelongpoincareformula
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A geometric proof of the Lelong-Poincaré formula

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