A multiple cut operation on a symplectic manifold produces a collection of cut spaces. In this talk I explain, using examples, how pseudoholomorphic curves degenerate under a multiple cut into broken curves. If time permits, I will also talk about a further degeneration of broken curves similar in spirit to Bourgeois' version of symplectic field theory and the Fulton-Sturmfels degeneration of the diagonal in a toric variety.
