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Twisted holomorphic symplectic forms

Twisted holomorphic symplectic forms We show that a compact Kähler manifold admitting a non‐degenerate holomorphic 2‐form valued in a line bundle is a finite cyclic cover of a hyperkähler manifold. With respect to the connection induced by the locally hyperkähler metric, the form is parallel. We then describe the structure of the fundamental group of such manifolds and derive some consequences. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Twisted holomorphic symplectic forms

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References (12)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdw039
Publisher site
See Article on Publisher Site

Abstract

We show that a compact Kähler manifold admitting a non‐degenerate holomorphic 2‐form valued in a line bundle is a finite cyclic cover of a hyperkähler manifold. With respect to the connection induced by the locally hyperkähler metric, the form is parallel. We then describe the structure of the fundamental group of such manifolds and derive some consequences.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Oct 1, 2016

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