Abstract
We announce the structure theorem for theH 2(M)-generated part of cohomology of a compact hyperkähler manifold. This computation uses an action of the Lie algebra so(4,n−2) wheren=dimH 2(M) on the total cohomology space ofM. We also prove that every two points of the connected component of the moduli space of holomorphically symplectic manifolds can be connected with so-called “twistor lines” — projective lines holomorphically embedded in the moduli space and corresponding to the hyperkähler structures. This has interesting implications for the geometry of compact hyperkähler manifolds and of holomorphic vector bundles over such manifolds.
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Verbitsky, M. Cohomology of compact hyperkähler manifolds and its applications. Geometric and Functional Analysis 6, 601–611 (1996). https://doi.org/10.1007/BF02247112
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DOI: https://doi.org/10.1007/BF02247112