On reprensentation theory and the cohomology rings of irreducible compact hyper-Kähler manifolds of complex dimension four
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)].
scientific article; zbMATH DE number 2028889
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