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The structure of birational maps between algebraic varieties becomes increasingly complicated as the dimension of the varieties increases. There is no birational geometry to speak of in dimension one: if two complete algebraic curves are birationally isomorphic then they are biregularly isomorphic. In dimension two we encounter the phenomenon of the blowup of a point, and every birational isomorphism can be factored into a sequence of blowups and blowdowns. In dimension three, however, we first encounter birational maps which are biregular outside of a subvariety of codimension two (called the center of the birational map). When the center has a neighborhood with trivial canonical bundle, the birational map is called a flop. The focus of this paper will be the case of a three-dimensional simple flop, in which the center is an irreducible curve (necessarily a smooth rational curve). One of the motivations for studying this case is a theorem of Kawamata , which says that all birational maps between Calabi–Yau threefolds can be expressed as the composition of simple flops (in fact, of simple flops between nonsingular varieties).