Some computations on trivial canonical-bundle solvmanifolds

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.

References in corpus (9)

• On the $\partial \overline{\partial }$-Lemma and Bott-Chern cohomology
• Non-Kähler Calabi-Yau manifolds
• On products of harmonic forms
• Bott-Chern cohomology of solvmanifolds
• On Bott-Chern cohomology and formality
• On the Structure of Double Complexes
• Complex structures of splitting type
• On the canonical bundle of complex solvmanifolds and applications to hypercomplex geometry
• Pluripotential Homotopy Theory