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.

Keywords

• 14C05
• 32C30
• 32J25
• 53C65
• 58A25
• Complex projective space,Homogeneous space
• Chow divisor
• Cycle space
• Radon transform
• John differential equations
• Closed positive current
• Slicing
• Dual subvariety