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arXiv · 2403.10126

$\partial\bar{\partial}$-Lemma and $p$-K\"ahler structures on families of solvmanifolds

Andrea Cattaneo·Adriano Tomassini
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Abstract

We provide families of compact $(n + 1)$-dimensional complex non K\"ahler manifolds satisfying the $\partial\bar{\partial}$-Lemma, with holomoprhically trivial canonical bundle, carrying a balanced metric and with no $p$-K\"ahler structures. Such a construction extends to the completely solvable case in any dimension Nakamura's construction of low-dimensional holomorphically parallelizable solvmanifolds.

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Andrea Cattaneo, Adriano Tomassini. 2024-03-15. $\partial\bar{\partial}$-Lemma and $p$-K\"ahler structures on families of solvmanifolds. https://arxiv.org/abs/2403.10126

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