Geometry and Automorphisms of Non-Kähler Holomorphic Symplectic Manifolds

  title={Geometry and Automorphisms of Non-K{\"a}hler Holomorphic Symplectic Manifolds},
  author={Fedor A. Bogomolov and Nikon Kurnosov and Alexandra Kuznetsova and Egor Yasinsky},
  journal={arXiv: Algebraic Geometry},
We consider the only one known class of non-Kahler irreducible holomorphic symplectic manifolds, described in the works of D. Guan and the first author. Any such manifold $Q$ of dimension $2n-2$ is obtained as a finite degree $n^2$ cover of some non-Kahler manifold $W_F$ 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… Expand
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