The factorization theorem of toric birational maps and its toroidal extension

One of the long standing and difficult problems of algebraic geometry is the factorization problem. The factorization problem is concerned with the question of whether we can factorize a given proper birational morphism f : X → Y, where X and Y are nonsingular complete varieties, as a composition of blowups and blowdowns along smooth loci. In this thesis we give a complete and coherent presentation of Morelli\u27s brilliant treatment of this question in the context of toric morphisms, and extend it to the case of toroidal morphisms