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We construct closed complex submanifolds of which are differential but not
holomorphic complete intersections. We also prove a homotopy principle concerning the
removal of intersections with certain complex subvarieties of .
In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.
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