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arXiv · 2412.06588

Some computations on trivial canonical-bundle solvmanifolds

Lapo Rubini
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Abstract

We compute the Dolbeault and the Bott-Chern cohomology of six dimensional solvmanifolds endowed with a complex structure of splitting type, introduced by Kasuya, and with trivial canonical bundle. We build, following results by Angella and Kasuya, finite dimensional double subcomplexes $(C_\Gamma^{\bullet,\bullet},\partial,\bar{\partial})\subseteq(\wedge^{\bullet,\bullet}G/\Gamma,\partial,\bar{\partial})$ for which the inclusion is an isomorphism in cohomology. We decompose such double complexes into indecomposable ones. Lastly, we study some notions of formality for this class of manifolds, giving a characterization of the $\partial\bar{\partial}$-Lemma property in general complex dimension, and we compute triple ABC-Massey products on them.

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Lapo Rubini. 2024-12-09. Some computations on trivial canonical-bundle solvmanifolds. https://doi.org/10.1016/j.geomphys.2025.105586

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