Normal Crossings Degenerations of Symplectic Manifolds
  We use local Hamiltonian torus actions to degenerate a symplectic manifold to a normal crossings symplectic variety in a smooth one-parameter family. This construction, motivated in part by the Gross-Siebert and B. Parker's programs, contains a multifold version of the usual (two-fold) symplectic cut construction and in particular splits a symplectic manifold into several symplectic manifolds containing normal crossings symplectic divisors with shared irreducible components in one step. 
Mohammad Farajzadeh Tehrani and Aleksey Zinger
math.SG hep-th math.AG