Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909805499645952 |
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| author | Lusetti, Francesca Tomassini, Adriano |
| author_facet | Lusetti, Francesca Tomassini, Adriano |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds Lusetti, Francesca Tomassini, Adriano Differential Geometry 53C15, 53D05 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. |
| title | Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds |
| topic | Differential Geometry 53C15, 53D05 |
| url | https://arxiv.org/abs/2501.13179 |