Geometry and Automorphisms of Non-Kähler Holomorphic Symplectic Manifolds

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