Geometry and Automorphisms of Non-Kähler Holomorphic Symplectic Manifolds

Fedor Bogomolov, Nikon Kurnosov, Alexandra Kuznetsova, Egor Yasinsky

Research output: Contribution to journalArticlepeer-review


We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works by D. Guan and the 1st author. Any such manifold Q of dimension 2n-2 is obtained as a finite degree n2 cover of some non-Kähler manifold WF, which we call the base of Q. We show that the algebraic reduction of Q and its base is the projective space of dimension n-1. Besides, we give a partial classification of submanifolds in Q, describe the degeneracy locus of its algebraic reduction and prove that the automorphism group of Q satisfies the Jordan property.

Original languageEnglish (US)
Pages (from-to)12302-12341
Number of pages40
JournalInternational Mathematics Research Notices
Issue number16
StatePublished - Aug 1 2022

ASJC Scopus subject areas

  • General Mathematics


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