A {̄∂}∂–Poincaré lemma for forms near an isolated complex singularity

Harris, Adam; Tonegawa, Yoshihiro

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

A $\bar \{\partial \}\partial$–Poincaré lemma for forms near an isolated complex singularity
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by Adam Harris and Yoshihiro Tonegawa PDF

Proc. Amer. Math. Soc. 131 (2003), 3329-3334 Request permission

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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