Intersection of positive closed currents of higher bidegree

TL;DR

This paper proves that the wedge product of certain positive closed currents with continuous super-potentials on a compact Kähler manifold is itself a positive closed current, extending the understanding of intersection theory in complex geometry.

Contribution

It establishes that the wedge product of positive closed currents with continuous super-potentials is positive and closed, generalizing previous results in complex intersection theory.

Findings

Wedge product of currents is positive and closed under given conditions.

Extension of intersection theory for currents with continuous super-potentials.

Validates the wedge product definition by Dinh and Sibony in broader contexts.

Abstract

Let $X$ be a compact K\"ahler manifold of dimension $n.$ Let $T$ and $S$ be two positive closed currents on $X$ of bidegree $(p,p)$ and $(q,q)$ respectively with $p+q\le n.$ Assume that $T$ has a continuous super-potential. We prove that the wedge product $T \wedge S,$ defined by Dinh and Sibony, is a positive closed current.