A ∂∂-Poincaré Lemma for forms near an isolated complex singularity

A Harris; Y Tonegawa

doi:10.1090/S0002-9939-03-06875-8

A ∂∂-Poincaré Lemma for forms near an isolated complex singularity

A Harris
, Y Tonegawa

Mathematics

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

Abstract

Let X be an analytic subvariety of complex Euclidean space with isolated singularity at the origin, and let η be a smooth form of type (1.1) defined on X\{0}. The main result of this note is a criterion for solubility of the equation ∂∂u = η. This implies a criterion for triviality of a Hermitian– holomorphic line bundle (L,h) --> X\{0} in a neighbourhood of the origin.

Original language	English
Pages (from-to)	3329-3334
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-03-06875-8
Publication status	Published - 2003

Keywords

Real and Complex Functions (incl Several Variables)

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10.1090/S0002-9939-03-06875-8

https://hdl.handle.net/1959.11/942

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title = "A ∂∂-Poincar{\'e} Lemma for forms near an isolated complex singularity",

abstract = "Let X be an analytic subvariety of complex Euclidean space with isolated singularity at the origin, and let η be a smooth form of type (1.1) defined on X\textbackslash{}\{0\}. The main result of this note is a criterion for solubility of the equation ∂∂u = η. This implies a criterion for triviality of a Hermitian{\textendash} holomorphic line bundle (L,h) --> X\textbackslash{}\{0\} in a neighbourhood of the origin.",

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T1 - A ∂∂-Poincaré Lemma for forms near an isolated complex singularity

AU - Harris, A

AU - Tonegawa, Y

PY - 2003

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N2 - Let X be an analytic subvariety of complex Euclidean space with isolated singularity at the origin, and let η be a smooth form of type (1.1) defined on X\{0}. The main result of this note is a criterion for solubility of the equation ∂∂u = η. This implies a criterion for triviality of a Hermitian– holomorphic line bundle (L,h) --> X\{0} in a neighbourhood of the origin.

AB - Let X be an analytic subvariety of complex Euclidean space with isolated singularity at the origin, and let η be a smooth form of type (1.1) defined on X\{0}. The main result of this note is a criterion for solubility of the equation ∂∂u = η. This implies a criterion for triviality of a Hermitian– holomorphic line bundle (L,h) --> X\{0} in a neighbourhood of the origin.

KW - Real and Complex Functions (incl Several Variables)

U2 - 10.1090/S0002-9939-03-06875-8

DO - 10.1090/S0002-9939-03-06875-8

M3 - Article

SN - 0002-9939

VL - 131

SP - 3329

EP - 3334

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

A ∂∂-Poincaré Lemma for forms near an isolated complex singularity

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