Monomialization of Strongly Prepared Morphisms to Surfaces
Author | : Olga S. Kashcheyeva |
Publisher | : |
Total Pages | : 202 |
Release | : 2003 |
ISBN-10 | : OCLC:53987554 |
ISBN-13 | : |
Rating | : 4/5 (54 Downloads) |
Book excerpt: Monomialization of morphisms is the problem of transforming a mapping into a monomial mapping by blowing up a chain of nonsingular subvarieties in its domain and image. The notion of a strongly prepared morphism, a morphism with some local properties, was first introduced by S.D. Cutkosky in his paper on monomialization of morphisms from 3-folds to surfaces. As an intermediate result it was proved that after performing a finite sequence of blowups one can make every dominant morphism from a 3-fold to a surface strongly prepared. The similar result for higher dimensions is unknown. We prove that strongly prepared morphisms from n-folds to surfaces can be monomialized.