Hodge structures on cohomology algebras and geometry
Abstract
We study restrictions on cohomology algebras of Kaehler compact manifolds, not depending on the hp,q numbers or the symplectic structure. To illustrate the effectiveness of these restrictions, we give a number of examples of compact symplectic manifolds satisfying the Lefschetz property but not having the cohomology algebra of a compact Kaehler manifold. We also prove the stability of these restrictions under products.
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