Algebraic Cycles as Residues of Meromorphic Forms

According to a classical result of Weil [15], a divisor α of a smooth n-dimensional projective variety X is homologous to zero if and only if it is the residue of a closed meromorphic 1-form on X. Griffiths proved recently [9, pp. 3-8] that a 0-cycle α of X is homologous to zero if and only if it is...

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Detalles Bibliográficos
Autores principales: Coleff, Nicolás, Herrera, M., Lieberman, D.
Formato: Articulo
Lenguaje:Inglés
Publicado: 1980
Materias:
Matemática
Ciencias Exactas
Residual Complex
Poincaré isomorphism
Algebraic Cycles
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/139838
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-139838
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Ciencias Exactas
Residual Complex
Poincaré isomorphism
Algebraic Cycles
spellingShingle Matemática
Ciencias Exactas
Residual Complex
Poincaré isomorphism
Algebraic Cycles
Coleff, Nicolás
Herrera, M.
Lieberman, D.
Algebraic Cycles as Residues of Meromorphic Forms
topic_facet Matemática
Ciencias Exactas
Residual Complex
Poincaré isomorphism
Algebraic Cycles
description According to a classical result of Weil [15], a divisor α of a smooth n-dimensional projective variety X is homologous to zero if and only if it is the residue of a closed meromorphic 1-form on X. Griffiths proved recently [9, pp. 3-8] that a 0-cycle α of X is homologous to zero if and only if it is the Grothendieck residue of a meromorphic n-form ώ on X having poles in the union of a family of complex hypersurfaces Y1 . . . . . Yn, of X, such that ∩ Yi is 0-dimensional and contains the support of α. We show in this paper (Theorem 3.7) that, in fact, any q-dimensional algebraic cycle α of X, 0≦ q ≦ n, is the analytic residue of a semimeromorphic (n-q)-form ώ on X, having poles in the union of a family F = {Y1 . . . . . Yn-q} of hypersurfaces in X such that ∩ F contains the support of α.
format Articulo
Articulo
author Coleff, Nicolás
Herrera, M.
Lieberman, D.
author_facet Coleff, Nicolás
Herrera, M.
Lieberman, D.
author_sort Coleff, Nicolás
title Algebraic Cycles as Residues of Meromorphic Forms
title_short Algebraic Cycles as Residues of Meromorphic Forms
title_full Algebraic Cycles as Residues of Meromorphic Forms
title_fullStr Algebraic Cycles as Residues of Meromorphic Forms
title_full_unstemmed Algebraic Cycles as Residues of Meromorphic Forms
title_sort algebraic cycles as residues of meromorphic forms
publishDate 1980
url http://sedici.unlp.edu.ar/handle/10915/139838
work_keys_str_mv AT coleffnicolas algebraiccyclesasresiduesofmeromorphicforms
AT herreram algebraiccyclesasresiduesofmeromorphicforms
AT liebermand algebraiccyclesasresiduesofmeromorphicforms
bdutipo_str Repositorios
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