Lifts of Lagrangian tori (Q2435827)

In this paper the Lagrangian geometry of compact symplectic varieties possessing a pseudotoric structure is studied. In particular the problem of constructing Lagrangian tori is considered. The main observation of the present paper is as follows. If a regular pseudotoric structure \(Y\) be defined on a compact symplectic variety \(X\), then for arbitrary smooth Lagrangian torus \(T \in Y\) there are exists a lift of \(T\) to a smooth Lagrangian torus \(T(x) \in X\). Next, some conditions and restrictions on this observation are considered and an example is offered.