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arXiv · 2501.13179

Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds

Francesca Lusetti·Adriano Tomassini
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Abstract

We provide new families of compact complex manifolds with no Kähler structure carrying symplectic structures satisfying the \textit{Hard Lefschetz Condition}. These examples are obtained as compact quotients of the solvable Lie group $\mathbb{C}^{2n} \ltimes_ρ \mathbb{C}^{2m}$, for which we construct explicit lattices. By cohomological computations we prove that such manifolds carry symplectic structures satisfying the \textit{Hard Lefschetz Condition}. Furthermore, we compute the Kodaira dimension of an almost-Kähler structure and generators for the de Rham and Dolbeault cohomologies.

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Francesca Lusetti, Adriano Tomassini. 2025-09-25. Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds. https://arxiv.org/abs/2501.13179

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