Intersections of Quadrics, Moment-Angle Manifolds, and Hamiltonian-Minimal Lagrangian Embeddings

We study the topology of Hamiltonian-minimal Lagrangian submanifolds $N$ in $\mathbb{C}^m$ constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the well-known Delzant construction of Hamiltonian toric manifolds. We establish the following topological properties of $N$: every $N$ embeds as a submanifold in the corresponding moment-angle manifold $\mathcal Z$, and every $N$ is the total space of two different fibrations, one over the torus $T^{m-n}$ with fiber a real moment-angle manifold $\mathcal{R}$ and the other over a quotient of $\mathcal{R}$ by a finite group with fiber a torus. These properties are used to produce new examples of Hamiltonian-minimal Lagrangian submanifolds with quite complicated topology.