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Finiteness results for hyperkaehler manifolds

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arxiv math/0109024 v1 pith:XDZILSVI submitted 2001-09-04 math.AG math.DG

Daniel Huybrechts This is my paper · ORCID
classification math.AGmath.DG
keywords finitenesshyperkaehlermanifoldssecondchernclasscohomologycompact
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In this short note we prove that the number of deformation types of compact hyperkaehler manifolds with prescribed second cohomology and second Chern class is finite. The proof uses the finiteness result of Kollar and Matsusaka, a formula by Hitchin and Sawon and the surjectivity of the period map.

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  1. Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum

    math.AG 2019-08 conditional novelty 6.0 of 10

    Corrected proofs for the global Torelli theorem for hyperkähler manifolds are supplied by switching from the Teichmüller space to the marked moduli space and by adding an ergodic lemma on lattice isometry groups.

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