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.
@article{bwmeta1.element.doi-10_1515_coma-2017-0008,
author = {Michel M\'eo},
title = {Regularization of closed positive currents and intersection theory},
journal = {Complex Manifolds},
volume = {4},
year = {2017},
pages = {120-136},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0008}
}
Michel Méo. Regularization of closed positive currents and intersection theory. Complex Manifolds, Tome 4 (2017) pp. 120-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0008/