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arXiv · 1507.03385

Complex structures of splitting type

Daniele Angella·Antonio Otal·Luis Ugarte·Raquel Villacampa
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Abstract

We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they allow us to construct a countable family of compact complex non-$\partial\overline\partial$ manifolds $X_k$, $k\in\mathbb{Z}$, that admit a small holomorphic deformation $\{(X_{k})_{t}\}_{t\inΔ_k}$ satisfying the $\partial\overline\partial$-Lemma for any $t\inΔ_k$ except for the central fibre. Moreover, a study of the existence of special Hermitian metrics is also carried out on six-dimensional solvmanifolds with splitting-type complex structures.

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Daniele Angella, Antonio Otal, Luis Ugarte, Raquel Villacampa. 2016-04-27. Complex structures of splitting type. https://doi.org/10.4171/rmi%2F973

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