Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

Abstract

We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in 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 Z, and every N is the total space of two different fibrations, one over the torus T^{m-n} with fibre a real moment-angle manifold R, and another over a quotient of R by a finite group with fibre a torus. These properties are used to produce new examples of Hamiltonian-minimal Lagrangian submanifolds with quite complicated topology.