Some computations on trivial canonical-bundle solvmanifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909953928724480 |
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| author | Rubini, Lapo |
| author_facet | Rubini, Lapo |
| contents | 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 $(C_Γ^{\bullet,\bullet},\partial,\bar{\partial})\subseteq(\wedge^{\bullet,\bullet}G/Γ,\partial,\bar{\partial})$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some computations on trivial canonical-bundle solvmanifolds Rubini, Lapo Differential Geometry Complex Variables 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 $(C_Γ^{\bullet,\bullet},\partial,\bar{\partial})\subseteq(\wedge^{\bullet,\bullet}G/Γ,\partial,\bar{\partial})$ 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. |
| title | Some computations on trivial canonical-bundle solvmanifolds |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2412.06588 |