A morphism of algebraic varieties is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mapping. This book proves that a domin... » 

A morphism of algebraic varieties is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mapping. This book proves that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by sequences of blowups of nonsingular subvarieties of X and S. «