Lelong Numbers of Bidegree (1,1) Currents on Multiprojective Spaces

2019/01/31 by Dan Coman, Coman, Dan, James J. Heffers +1
Computer Science · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1901.11157

openalex publication_date 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a positive closed current of bidegree (1,1) on a multiprojective space X=\mathbb P^n₁×…×\mathbb P^n_k. For certain values of α, which depend on the cohomology class of T, we show that the set of points of X where the Lelong numbers of T exceed α have certain geometric properties. We also describe the currents T that have the largest possible Lelong number in a given cohomology class, and the set of points where this number is assumed.

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