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Regularization of closed positive currents and intersection theory

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Méo M.

Complex Manifolds

2017

tom 4

nr 1

120-136

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.

Ograniczanie wyników

1 Complex Manifolds

1 Méo M.

1 2017

Wyniki wyszukiwania

Regularization of closed positive currents and intersection theory