arXiv subjects

James J. Heffers

Publications and source records attributed to James J. Heffers.

2 recordsLinked to original sources

arXiv2018

On Lelong Numbers of Positive Closed Currents on $\mathbb{P}^n$

Let $T$ be a positive closed current of bidimension $(p,p)$ with unit mass on the complex projective space $\mathbb P^n$. For certain values of $α$ and $β= β(p, α)$ we show that if $T$ has enough points where the Lelong number is at least $α$, then the upper level set $E_β^+ (T)$ of points where $T$ has Lelong number strictly larger than $β$ has certain geometric properties.

math.CV↗

arXiv2017

A Property of Upper Level Sets of Lelong Numbers of Currents on $\mathbb{P}^2$

Let $T$ be a positive closed current of bidimension $(1,1)$ with unit mass on the complex projective space $\mathbb P^2$. For $α> 2/5$ and $β= (2-2α)/3$ we show that if $T$ has four point with Lelong number greater than $α$, the upper level set $E_β^+ (T)$ of points of $T$ with Lelong number strictly larger than $β$ is contained within a conic with the exception of at most one point.

math.CV↗