Hodge structures on cohomology algebras and geometry

2007/03/18 by Voisin, Claire
Mathematics · #14C30 #32J27 #53D05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · doi:10.48550/arxiv.math/0703523

openalex publication_date 2007/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Cohomological aspects of non-Kähler manifolds
• Compatible almost complex structures on the Hard Lefschetz condition
• Hard Lefschetz property of symplectic structures on compact Kaehler manifolds
• On the Lefschetz and Hodge-Riemann theorems
• Mixed Hodge formality