Regularization of closed positive currents and intersection theory

We prove the existence of a closed regularization of the integration current associated to an effective analytic cycle, with a bounded negative part. By means of the King formula, we are reduced to regularize a closed differential form with L1loc coefficients, which by extension has a test value on...

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Autor principal:	Méo Michel
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	chern class green operator macpherson graph construction modification positive current residue current 14c17 32c30 32j25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ebb1e10aadbd43d986850742c610a820
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spelling	oai:doaj.org-article:ebb1e10aadbd43d986850742c610a8202021-12-02T16:36:59ZRegularization of closed positive currents and intersection theory2300-744310.1515/coma-2017-0008https://doaj.org/article/ebb1e10aadbd43d986850742c610a8202017-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2017-0008https://doaj.org/toc/2300-7443We prove the existence of a closed regularization of the integration current associated to an effective analytic cycle, with a bounded negative part. By means of the King formula, we are reduced to regularize a closed differential form with L1loc coefficients, which by extension has a test value on any positive current with the same support as the cycle. As a consequence, the restriction of a closed positive current to a closed analytic submanifold is well defined as a closed positive current. Lastly, given a closed smooth differential (qʹ, qʹ)-form on a closed analytic submanifold, we prove the existence of a closed (qʹ, qʹ)-current having a restriction equal to that differential form. After blowing up we deal with the case of a hypersurface and then the extension current is obtained as a solution of a linear differential equation of order 1.Méo MichelDe Gruyterarticlechern classgreen operatormacpherson graph constructionmodificationpositive currentresidue current14c1732c3032j25MathematicsQA1-939ENComplex Manifolds, Vol 4, Iss 1, Pp 120-136 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	chern class green operator macpherson graph construction modification positive current residue current 14c17 32c30 32j25 Mathematics QA1-939
spellingShingle	chern class green operator macpherson graph construction modification positive current residue current 14c17 32c30 32j25 Mathematics QA1-939 Méo Michel Regularization of closed positive currents and intersection theory
description	We prove the existence of a closed regularization of the integration current associated to an effective analytic cycle, with a bounded negative part. By means of the King formula, we are reduced to regularize a closed differential form with L1loc coefficients, which by extension has a test value on any positive current with the same support as the cycle. As a consequence, the restriction of a closed positive current to a closed analytic submanifold is well defined as a closed positive current. Lastly, given a closed smooth differential (qʹ, qʹ)-form on a closed analytic submanifold, we prove the existence of a closed (qʹ, qʹ)-current having a restriction equal to that differential form. After blowing up we deal with the case of a hypersurface and then the extension current is obtained as a solution of a linear differential equation of order 1.
format	article
author	Méo Michel
author_facet	Méo Michel
author_sort	Méo Michel
title	Regularization of closed positive currents and intersection theory
title_short	Regularization of closed positive currents and intersection theory
title_full	Regularization of closed positive currents and intersection theory
title_fullStr	Regularization of closed positive currents and intersection theory
title_full_unstemmed	Regularization of closed positive currents and intersection theory
title_sort	regularization of closed positive currents and intersection theory
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/ebb1e10aadbd43d986850742c610a820
work_keys_str_mv	AT meomichel regularizationofclosedpositivecurrentsandintersectiontheory
_version_	1718383665879187456

Regularization of closed positive currents and intersection theory

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