Poincaré lemma for tangential Cauchy Riemann complexes
type: Item
instance of: scholarly article
title: Poincaré lemma for tangential Cauchy Riemann complexes
zbMATH Open document ID: 0574.32045
DOI: 10.1007/BF01451852
published in: Mathematische Annalen
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/182931
review text: The author studies the tangential Cauchy-Riemann complex of a generic real submanifold S of a complex manifold X. The Levi form of S at \(x_ 0\in S\) is a quadratic form on the analytic tangent space \(H_{x_ 0}S\) with values in \(T_{x_ 0}S/H_{x_ 0}S\). For \(x_ 0\in S\), the set \(E(S,x_ 0)\) is defined with the help of the Levi form: \(E(S,x_ 0)\) is a set of pairs of non-negative integers (p,q) with \(p+q\leq \dim_{{\mathbb{C}}}H_{x_ 0}S.\) \(E(S,x_ 0)\) is a local pseudoconformal invariant on S. The author shows: If \(p_ 0=\min imum p: (p,q)\in E(s,x_ 0)\) then the tangential Cauchy-Riemann complex admits the Poincaré lemma at j wherever \(1\leq j<p_ 0\) and \(j>\dim_{{\mathbb{C}}}H_{x_ 0}-p_ 0.\) The approach in the proof follows ideas of \textit{A. Andreotti} and \textit{H. Grauert} in Bull. Soc. Math. Fr. 90, 193-259 (1962; Zbl 0106.055).
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32C36
Mathematics Subject Classification ID: 58J10
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 3916736
zbMATH Keywords: sheaves of germs of differential forms
zbMATH Keywords: tangential Cauchy-Riemann complex
zbMATH Keywords: real submanifold
zbMATH Keywords: complex manifold
zbMATH Keywords: Levi form
zbMATH Keywords: Poincaré lemma
author: Mauro Nacinovich
MaRDI profile type: Publication
Wikidata QID: Q124968553
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description: scientific article; zbMATH DE number 3916736