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A $\bar{\partial}\partial$-Poincaré lemma for forms near an isolated complex singularity

Authors: Adam Harris and Yoshihiro Tonegawa
Journal: Proc. Amer. Math. Soc. 131 (2003), 3329-3334
MSC (2000): Primary 14J17, 32B15, 32S05, 32W05
Published electronically: February 20, 2003
MathSciNet review: 1990620
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Abstract: Let $X$ be an analytic subvariety of complex Euclidean space with isolated singularity at the origin, and let $\eta$ be a smooth form of type $(1.1)$ defined on $X \setminus\{0\}$. The main result of this note is a criterion for solubility of the equation $\bar{\partial}\partial u = \eta$. This implies a criterion for triviality of a Hermitian- holomorphic line bundle $(L,h)\to X\setminus\{0\}$ in a neighbourhood of the origin.

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Additional Information

Adam Harris
Affiliation: Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia
Address at time of publication: Department of Mathematics & Computer Science, University of New England, Armidale, New South Wales 2351, Australia

Yoshihiro Tonegawa
Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

Received by editor(s): September 18, 2001
Received by editor(s) in revised form: June 1, 2002
Published electronically: February 20, 2003
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2003 American Mathematical Society