Geometry and automorphisms of nonKähler holomorphic symplectic manifolds
Abstract
We consider the only one known class of nonKähler irreducible holomorphic symplectic manifolds, described in the works of D. Guan and the first author. Any such manifold $Q$ of dimension $2n2$ is obtained as a finite degree $n^2$ cover of some nonKähler 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 $n1$. 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.01193
 Bibcode:
 2020arXiv200501193B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 14J42;
 53D05;
 53C26;
 32C15;
 32C25;
 32H04;
 32Q99;
 32M18;
 14K99
 EPrint:
 29 pages