Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds

Fuente: arXiv
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Main Authors: Lusetti, Francesca, Tomassini, Adriano
Format: Preprint
Published: 2025
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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
id 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