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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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2017
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/ebb1e10aadbd43d986850742c610a820 |
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| Sumario: | 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. |
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