Regularization of closed positive currents and intersection theory

• Autorzy: Michel Méo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 14C17: Intersection theory, characteristic classes, intersection multiplicities
• 32J25: Transcendental methods of algebraic geometry
• 32C30: Integration on analytic sets and spaces, currents

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 120-136

Daty

wydano

2017-02-23

otrzymano

2016-12-23

zaakceptowano

2017-06-26

online

2017-07-20

Twórcy

autor

Michel Méo

• ,

Identyfikatory

DOI

10.1515/coma-2017-0008