Cohomology vanishing theorems on weakly 1-complete manifolds
type: Item
instance of: scholarly article
title: Cohomology vanishing theorems on weakly 1-complete manifolds
zbMATH Open document ID: 0537.32014
author: Takeo Ohsawa
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1983-01-01T00:00:00Z
review text: A survey article on the vanishing theorems on weakly 1-complete manifolds which are obtained mainly in the 70's by S. Nakano, O. Abdelkader, etc., based on the \(L^ 2\)-method of Andreotti-Vesentini. A new and simple proof is given to Nakano's vanishing theorem for the cohomology group of bi-degree (p,q) with coefficients in positive line bundles. Applications to classical problems such as the inverse of monoidal transformation are given, but not in detail. In sublemma 2, there is a misprint. \(''\{c_ k\}_{k\geq m}\) is monotonically decreasing'' should read \(''\{c_ k^{1/k}\}_{k\geq m}\) is monotonically decreasing''.
Mathematics Subject Classification ID: 32L20
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32E05
Mathematics Subject Classification ID: 32L10
zbMATH DE Number: 3853485
zbMATH Keywords: Nakano vanishing theorem
zbMATH Keywords: weakly 1-complete manifolds
zbMATH Keywords: inverse of monoidal transformation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195182026
OpenAlex ID: W2036059968
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DOI: 10.2977/PRIMS/1195182026
description: scientific article; zbMATH DE number 3853485