arXiv subjects

Lapo Rubini

Publications and source records attributed to Lapo Rubini.

3 recordsLinked to original sources

arXiv2026

Holomorphically parallelizable solvmanifolds with special metrics and their deformations

We investigate the existence of strong K\"ahler with torsion metrics along deformations of the Iwasawa manifold and of the holomorphically parallelizable Nakamura manifold. We also show that the class of deformations of the holomorphically parallelizable Nakamura manifold yielding a non-left-invariant complex structure admits a balanced metric but does not admit any strong K\"ahler with torsion metric. We then construct the Kuranishi space of a $4$-dimensional holomorphically parallelizable solvmanifold and study whether small deformations of such a manifold admit SKT metrics. Finally, we provide some results concerning the existence of metrics satisfying $\partial \bar{\partial} \omega = 0$, $\partial \bar{\partial} \omega^2 = 0$ on a particular class of $2$-step nilpotent nilmanifolds.

math.DG↗

arXiv2026

Strong formality below middle degree implies strong formality

We show that hyperplane sections of strongly formal manifolds inherit strong formality. In particular, this property holds for generalized complete intersections defined by positive line bundles with trivial first de Rham cohomology group. Furthermore, we establish the strong formality of compact K\"ahler manifolds with central cohomology of width $\frac{n}{2}-1$ and, more generally, of compact $\partial\bar{\partial}$-manifolds with no non-trivial multiplicative relations in cohomology below degree $n+2$. These results arise from the notion of $s$-strong formality, which we adapt from a work of Fernandez and Mu\~noz to the pluripotential setting. Specifically, we prove that a compact, connected complex manifold of dimension $n$ with trivial first de Rham cohomology group is strongly formal if and only if it is $(n-1)$-strongly formal.

math.DG↗

arXiv2024

Some computations on trivial canonical-bundle solvmanifolds

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.

math.DG↗