Nontoric Foliations by Lagrangian Tori of Toric Fano Varieties

A construction of a foliation of a toric Fano variety by Lagrangian tori is presented; it is based on linear subsystems of divisor systems of various degrees invariant under the Hamiltonian action of distinguished function-symbols. It is shown that known examples of foliations (such as the Clifford foliation and D. Auroux's example) are special cases of this construction. As an application, nontoric Lagrangian foliations by tori of two-dimensional quadrics and projective space are constructed.