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Complex Manifolds

Ed. by Fino, Anna Maria

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Regularization of closed positive currents and intersection theory

Michel Méo
Published Online: 2017-07-20 | DOI: https://doi.org/10.1515/coma-2017-0008


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.

Keywords : Chern class; Green operator; MacPherson graph construction; Modification; Positive current; Residue current

MSC 2010: 14C17; 32C30; 32J25


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About the article

Received: 2016-12-23

Accepted: 2017-06-26

Published Online: 2017-07-20

Published in Print: 2017-02-23

Citation Information: Complex Manifolds, Volume 4, Issue 1, Pages 120–136, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2017-0008.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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