周变换的对偶

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2018-09-01 DOI:10.1515/coma-2018-0011

M. Meo

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引用次数: 1

摘要

在复射影空间上定义了电流的Chow变换的对偶。这个变换分解了Chow变换的左逆，它与Chow变换的组合是一个线性微分算子的右逆。这样，我们就完成了周氏变换的积分几何的一般格式。另一方面证明了与射影空间上的每一个闭正电流相关联的一个定义良好的闭正正规电流的存在性。这是定义在对偶射影空间上的对偶电流存在的结果。这使我们可以将已知的有效代数循环周氏除数法向量的反演公式推广到闭合正电流的情况。

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A Dual of the Chow Transformation

Abstract 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.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.