The second Betti number of hyperkähler manifolds

2014/01/02 by Kurnosov Nikon, Kurnosov, Nikon
Mathematics · #14K22 #53C26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1401.0510

openalex publication_date 2014/01/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let M be a compact irreducible hyperkahler manifold, from Bogomolov inequality [V1] we obtain forbidden values of the second Betti number b₂ 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 b₂ for hyperkähler manifolds.

Citations

• Finiteness results for hyperkaehler manifolds

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