Demailly-Lelong numbers on complex spaces
Complex Variables
2025-03-06 v2 Algebraic Geometry
Abstract
We prove a conjecture proposed by Berman-Boucksom-Eyssidieux-Guedj-Zeriahi, affirming that the Demailly-Lelong number can be determined through a combination of intersection numbers given by the divisorial part of the potential and the SNC divisors over a log resolution of the maximal ideal of a given point. Moreover, this result establishes a pointwise comparison of two different notions of Lelong numbers of plurisubharmonic functions defined on singular complex spaces. We also provide an estimate for quotient singularities and sharp estimates for two-dimensional ADE singularities.
Cite
@article{arxiv.2403.08620,
title = {Demailly-Lelong numbers on complex spaces},
author = {Chung-Ming Pan},
journal= {arXiv preprint arXiv:2403.08620},
year = {2025}
}
Comments
16 pages; v2: minor corrections based on the referee's comments; to appear in Math. Z