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Newton Numbers and Residual Measures of Plurisubharmonic Functions

Alexander Rashkovskii
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Abstract

We study the masses charged by $(dd^cu)^n$ at isolated singularity points of plurisubharmonic functions $u$. It is done by means of the local indicators of plurisubharmonic functions. 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 $u$.

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Alexander Rashkovskii. 1999-05-11. Newton Numbers and Residual Measures of Plurisubharmonic Functions. https://arxiv.org/abs/math/9905062

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