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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Defining equations for real analytic real hypersurfaces in $ {\bf C}\sp n$


Author: John P. D’Angelo
Journal: Trans. Amer. Math. Soc. 295 (1986), 71-84
MSC: Primary 32F25; Secondary 32C05
DOI: https://doi.org/10.1090/S0002-9947-1986-0831189-5
MathSciNet review: 831189
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Abstract: A defining function for a real analytic real hypersurface can be uniquely written as $ 2\operatorname{Re} (H) + E$, where $ H$ is holomorphic and $ E$ contains no pure terms. We study how $ H$ and $ E$ change when we perform a local biholomorphic change of coordinates, or multiply by a unit. One of the main results is necesary and sufficient conditions on the first nonvanishing homogeneous part of $ E$ (expanded in terms of $ H$) beyond $ {E_{00}}$ that serve as obstructions to writing a defining equation as $ 2\operatorname{Re} (h) + e$, where $ e$ is independent of $ h$. We also find necessary pluriharmonic obstructions to doing this, which arise from the easier case of attempting to straighten the hypersurface.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0831189-5
Article copyright: © Copyright 1986 American Mathematical Society