Twisted holomorphic symplectic forms
arXiv:1507.04713 · doi:10.1112/blms/bdw039
Abstract
We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the form is parallel. We then describe the structure of the fundamenal group of such manifolds and derive some consequences.
13 pages