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 $(C_{\hat{I}}{“}^{\bullet ,\bullet },\partial ,\bar{\partial })\subseteq ({\wedge }^{\bullet ,\bullet }G/\hat{I}“,\partial ,\bar{\partial })$ 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.