A note on the rank of positive closed currents

TL;DR

This paper provides an estimate on the rank of tangent vectors to positive closed currents in complex projective space, linking it to the dimension of their trace measures.

Contribution

It introduces a new estimate relating the rank of tangent vectors of positive closed currents to the trace measure dimension in CP^k.

Findings

Establishes an almost everywhere rank estimate for tangent vectors.

Connects tangent vector rank to trace measure dimension.

Provides a theoretical bound in complex geometry.

Abstract

In this short note we prove an estimate on the rank a.e. of the tangent (p,p) vector to a a positive closed current of bidimension (p,p) in CP^k, in terms of the dimension of its trace measure.