Demailly-Lelong numbers on complex spaces
arXiv:2403.08620 · doi:10.1007/s00209-024-03636-z
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.
16 pages; v2: minor corrections based on the referee's comments; to appear in Math. Z