A Dual of the Chow Transformation

We define a dual of the Chow transformation of currents on the complex projective space. This transformation factorizes a left inverse of the Chow transformation and its composition with the Chow transformation is a right inverse of a linear diferential operator. In such a way we complete the genera...

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Bibliographic Details
Main Author: Méo Michel
Format: Article
Language:English
Published: De Gruyter 2018-09-01
Series:Complex Manifolds
Subjects:
Online Access:http://www.degruyter.com/view/j/coma.2018.5.issue-1/coma-2018-0011/coma-2018-0011.xml?format=INT
Description
Summary:We define a dual of the Chow transformation of currents on the complex projective space. This transformation factorizes a left inverse of the Chow transformation and its composition with the Chow transformation is a right inverse of a linear diferential operator. In such a way we complete the general scheme of integral geometry for the Chow transformation. On another hand we prove the existence of a well defined closed positive conormal current associated to every closed positive current on the projective space. This is a consequence of the existence of a dual current, defined on the dual projective space. This allows us to extend to the case of a closed positive current the known inversion formula for the conormal of the Chow divisor of an effective algebraic cycle.
ISSN:2300-7443