Generically Finite Morphisms
Abstract
Description
We consider the problem of birationally modifying a morphism of complete varieties to make it a morphism from a nonsingular variety to a normal variety. Our main result is to give a counterexample to this problem. This example also is a counterexample to the related conjecture of Abhyankar on ``weak simultaneous global resolution''.
We also give some positive results. Forinstance, a positive result of this kind is possible if we remove the separatedness condition.