  Let $M$ be a compact irreducible hyperkahler manifold, from Bogomolov
inequality [V1] we obtain forbidden values of the second Betti number $b_2$ in
arbitrary dimension. UPD: Unfortunately, decomposition of dual to BBF-form is
not right in the main theorem. Instead of this work, take a look on recent
preprints of Sawon and me on boundedness of $b_2$ for hyperk\"ahler manifolds.
