Intersection of Positive Closed Currents

Abstract

We investigate the intersection of positive closed currents in a general setting, employing tangent currents alongside King's residue formula. Our main result establishes a natural condition for the intersection--namely, the Dinh-Sibony product--of positive closed currents on domains and derives an integral representation of this intersection. In parallel, we study the existence, $h$-dimension, and shadow of tangent currents, extending our approach to the study of the self-intersection of analytic subsets. We also present a local version of superpotentials and a regularization of positive closed currents, explore the connections with slicing theory, and examine classical examples. Our work extends to general complex manifolds, including compact Kähler manifolds.

arXiv commentchanged title. reduced length. more polished. Comments are very welcome!