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 - Funding Information:
This work was supported by the EPSRC programme grant [EP/M024830 to F.B.];
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.
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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 -