Francesca Lusetti | Searcharxiv

arXiv2026

Non-K\"ahler Special Lagrangian submanifolds and SYZ mirror symmetry

We determine purely algebraic equations to identify \textit{SLags} generated by invariant distributions in a class of non-K\"ahler Calabi-Yau manifolds. We determine SLag distributions, determine which leaves integrate to compact submanifolds and study the deformation theory, which we find to be unobstructed. We apply our results to the Iwasawa manifold, the completely solvable 6-dimensional Nakamura manifold and the complex parallelizable Nakamura manifold. Through these examples we find families of topologically distinct \textit{SLags}, including the existence of SLag torus fibrations. Following the proposal of Lau-Tseng-Yau, we compute the non-K\"ahler SYZ mirrors of Nakamura manifolds, together with their refined symplectic Bott-Chern cohomologies. As a consequence, we find the existence of semi-flat non-K\"ahler mirror pairs which are not diffeomorphic.

math.DG↗

arXiv2025

Hard Lefschetz Condition on symplectic non-K\"ahler solvmanifolds

We provide new families of compact complex manifolds with no K\"ahler structure carrying symplectic structures satisfying the \textit{Hard Lefschetz Condition}. These examples are obtained as compact quotients of the solvable Lie group $\mathbb{C}^{2n} \ltimes_{\rho} \mathbb{C}^{2m}$, for which we construct explicit lattices. By cohomological computations we prove that such manifolds carry symplectic structures satisfying the \textit{Hard Lefschetz Condition}. Furthermore, we compute the Kodaira dimension of an almost-K\"ahler structure and generators for the de Rham and Dolbeault cohomologies.

math.DG↗