A -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 | References | Similar Articles | Additional Information

Abstract: Let be an analytic subvariety of complex Euclidean space with isolated singularity at the origin, and let be a smooth form of type defined on . The main result of this note is a criterion for solubility of the equation . This implies a criterion for triviality of a Hermitian- holomorphic line bundle 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

Email:
harris@ms.unimelb.edu.au

**Yoshihiro Tonegawa**

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

Email:
tonegawa@math.sci.hokudai.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-03-06875-8

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