Certain classes of pluricomplex Green functions on ℂn

Dan Coman

doi:10.1007/s002090000126

Certain classes of pluricomplex Green functions on ℂⁿ

Dan Coman

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider (pluricomplex) Green functions defined on ℂⁿ, with logarithmic poles in a finite set and with logarithmic growth at infinity. For certain sets, we describe all the corresponding Green functions. The set of these functions is large and it carries a certain algebraic structure. We also show that for some sets no such Green functions exist. Our results indicate the fact that the set of poles should have certain algebro-geometric properties in order for these Green functions to exist.

Original language	English (US)
Pages (from-to)	111-122
Number of pages	12
Journal	Mathematische Zeitschrift
Volume	235
Issue number	1
DOIs	https://doi.org/10.1007/s002090000126
State	Published - Sep 2000
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s002090000126

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abstract = "We consider (pluricomplex) Green functions defined on ℂn, with logarithmic poles in a finite set and with logarithmic growth at infinity. For certain sets, we describe all the corresponding Green functions. The set of these functions is large and it carries a certain algebraic structure. We also show that for some sets no such Green functions exist. Our results indicate the fact that the set of poles should have certain algebro-geometric properties in order for these Green functions to exist.",

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AB - We consider (pluricomplex) Green functions defined on ℂn, with logarithmic poles in a finite set and with logarithmic growth at infinity. For certain sets, we describe all the corresponding Green functions. The set of these functions is large and it carries a certain algebraic structure. We also show that for some sets no such Green functions exist. Our results indicate the fact that the set of poles should have certain algebro-geometric properties in order for these Green functions to exist.

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Certain classes of pluricomplex Green functions on ℂⁿ

Abstract

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