A note on the rank of positive closed currents

2012/03/26 by Romain Dujardin, Dujardin, Romain
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1203.5821

This is a complement, not intended for publication, to my paper "Fatou directions along the Julia set for endomorphisms of CP^k" [arXiv:1006.0882]

arxiv created 2012/03/26 · arxiv updated 2012/03/28

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.

Citations

• Fatou directions along the Julia set for endomorphisms of CP^k

Related

• On Lelong Numbers of Positive Closed Currents on ℙⁿ
• Intersection of Positive Closed Currents
• Uniqueness of tangent currents for positive closed currents
• Polynomial hulls and positive currents
• Positive plurisubharmonic currents: Generalized Lelong numbers and Tangent theorems