A Property of upper level sets of Lelong numbers of currents on ℙ2-Reference-Cited by-同舟云学术

A Property of upper level sets of Lelong numbers of currents on ℙ2

Published:2017-12 Issue:14 Volume:28 Page:1750110
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Heffers James J.¹

Affiliation:

1. Syracuse University, 215 Carnegie Building, Syracuse University, Syracuse, NY 13422, USA

Abstract

Let [Formula: see text] be a positive closed current of bidimension [Formula: see text] with unit mass on the complex projective space [Formula: see text]. For [Formula: see text] and [Formula: see text] we show that if [Formula: see text] has four points with Lelong number at least [Formula: see text], the upper level set [Formula: see text] of points of [Formula: see text] with Lelong number strictly larger than [Formula: see text] is contained within a conic with the exception of at most one point.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X17501105

Reference13 articles.

1. Certain classes of pluricomplex Green functions on ${\mathbb C}^n$

2. Entire pluricomplex Green functions and Lelong numbers of projective currents

3. Quasiplurisubharmonic Green functions

4. Plurisubharmonic functions with singularities and affine invariants for finite sets in $\mathbb{C}^n$

5. Geometric properties of upper level sets of Lelong numbers on projective spaces

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3. Lelong numbers of bidegree (1, 1) currents on multiprojective spaces;Mathematische Zeitschrift;2019-11-07

4. On Lelong numbers of positive closed currents on;Complex Variables and Elliptic Equations;2018-04-17