TY - JOUR
T1 - Geometry and Automorphisms of Non-Kähler Holomorphic Symplectic Manifolds
AU - Bogomolov, Fedor
AU - Kurnosov, Nikon
AU - Kuznetsova, Alexandra
AU - Yasinsky, Egor
N1 - Publisher Copyright:
© 2021 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2022/8/1
Y1 - 2022/8/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85135776663&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85135776663&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnab043
DO - 10.1093/imrn/rnab043
M3 - Article
AN - SCOPUS:85135776663
SN - 1073-7928
VL - 2022
SP - 12302
EP - 12341
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 16
ER -