The second Betti number of hyperkähler manifolds

Abstract

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 hyperkähler manifolds.

7 pages. Major changes

References in corpus (4)

• Hyperholomorpic connections on coherent sheaves and stability
• Finiteness results for hyperkaehler manifolds
• Hyperholomorphic bundles
• Curvature and characteristic numbers of hyperkähler manifolds