Newton numbers and residual measures of plurisubharmonic functions

Volume 75 / 2000

Alexander Rashkovskii Annales Polonici Mathematici 75 (2000), 213-231 DOI: 10.4064/ap-75-3-213-231


We study the masses charged by $(dd^cu)^n$ at isolated singularity points of plurisubharmonic functions u. This is done by means of the local indicators of plurisubharmonic functions introduced in [15]. As a consequence, bounds for the masses are obtained in terms of the directional Lelong numbers of u, and the notion of the Newton number for a holomorphic mapping is extended to arbitrary plurisubharmonic functions. We also describe the local indicator of u as the logarithmic tangent to u.


  • Alexander Rashkovskii

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