Complete negatively pinched Kähler surfaces of finite volume
type: Item
instance of: scholarly article
title: Complete negatively pinched Kähler surfaces of finite volume
zbMATH Open document ID: 0661.53048
author: Hajime Tsuji
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: Let S be a 2-dimensional, complete negatively pinched Kähler manifold of finite volume. It is known that S is a quasi-projective surface and can be compactified as a normal projective space \(\hat S\) by providing each end point with one point. S is then called the Siu-Yau's one-point compactification. By means of the classification method of normal surface singularities with solvable local fundamental groups due to \textit{P. Wagreich} [Topology 11, 51-72 (1972; Zbl 0204.56404)], the author proves that \(\hat S\) has only almost simple elliptic singularities. It is also shown that the \(L^ 2\)-cohomology group \(H^*_{(2)}\) of S and the intersection homology group \(IH_*\) of \(\hat S\) are related with each other by \(H^ i_{(2)}(S)\simeq IH_{4-i}(\hat S),\) \(0\leq i\leq 4\).
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 4080334
zbMATH Keywords: pinching condition
zbMATH Keywords: Kähler manifold
zbMATH Keywords: finite volume
zbMATH Keywords: Siu-Yau's one-point compactification
zbMATH Keywords: cohomology group
zbMATH Keywords: intersection homology group
reviewed by: Tanjiro Okubo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227923
OpenAlex ID: W2052910195
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DOI: 10.2748/TMJ/1178227923
description: scientific article; zbMATH DE number 4080334