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arXiv · 2005.01193

Geometry and automorphisms of non-Kähler holomorphic symplectic manifolds

Fedor Bogomolov·Nikon Kurnosov·Alexandra Kuznetsova·Egor Yasinsky
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Abstract

We consider the only one known class of non-Kähler 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-Kähler 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 of its algebraic reduction, and prove that the automorphism group of $Q$ satisfies the Jordan property.

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Fedor Bogomolov, Nikon Kurnosov, Alexandra Kuznetsova, Egor Yasinsky. 2021-03-29. Geometry and automorphisms of non-Kähler holomorphic symplectic manifolds. https://doi.org/10.1093/imrn%2Frnab043

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