Hodge structures on cohomology algebras and geometry

Details Hodge structures on cohomology algebras and geometry Hodge structures on cohomology algebras and geometry

2007-03-18

arxiv.org/abs/math/0703523v3

Mathematics

Algebraic Geometry

Final version, to appear in Math. Annalen 2008

Scientific paper

We study restrictions on cohomology algebras of Kaehler compact manifolds, not depending on the h^{p,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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