  Hamiltonian minimality (H-minimality) for Lagrangian submanifolds is a
symplectic analogue of Riemannian minimality. A Lagrangian submanifold is
called H-minimal if the variations of its volume along all Hamiltonian vector
fields are zero. This notion was introduced in the work of Y.-G. Oh in
connection with the celebrated Arnold conjecture on the number of fixed points
of a Hamiltonian symplectomorphism. In the previous works the authors defined
and studied a family of H-minimal Lagrangian submanifolds in complex space
arising from intersections of Hermitian quadrics. Here we extend this
construction to define H-minimal submanifolds in toric varieties.
