On reprensentation theory and the cohomology rings of irreducible compact hyper-Kähler manifolds of complex dimension four
type: Item
instance of: scholarly article
title: On reprensentation theory and the cohomology rings of irreducible compact hyper-Kähler manifolds of complex dimension four
zbMATH Open document ID: 1049.53035
DOI: 10.2478/BF02475186
published in: Central European Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
review text: The author proves a result announced in [Math. Res. Lett. 8, No. 5--6, 663--669 (2001; Zbl 1011.53039)] about non-existence of a complex four-dimensional irreducible compact hyper-Kähler manifold with Betti numbers \(b_2=7\) and \(b_3=4\). The proof uses \textit{M. Verbitsky}'s description of the part of the cohomology ring of a compact irreducible hyper-Kähler manifold generated by \(H^2\) [see Geom. Funct. Anal. 6, No. 4, 601--611 (1996; Zbl 0861.53069)].
reviewed by: Adrian Langer
Mathematics Subject Classification ID: 53C26
Mathematics Subject Classification ID: 32J27
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 32Q55
zbMATH DE Number: 2028889
zbMATH Keywords: hyper-Kähler manifolds
zbMATH Keywords: Betti numbers
author: Daniel Guan
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.2478/bf02475186
OpenAlex ID: W2141439675
description: scientific article; zbMATH DE number 2028889