Local factorization and monomialization of morphisms
Algebraic Geometry
2007-05-23 v2 Commutative Algebra
Abstract
Suppose that X to Y is a generically finite map of nonsingular varieties over a field of characteristic zero, and v is a valuation of the function field of X. We prove that it is possible to perform a sequence of monoidal transforms X' to X and Y' to Y so that X' to Y' is a monomial mapping at the center of v. We deduce from this that a birational morphism of nonsingular varieties can be factored along a valuation by a sequence of blowups and blowdowns with nonsingular centers.
Keywords
Cite
@article{arxiv.math/9803078,
title = {Local factorization and monomialization of morphisms},
author = {Steven Dale Cutkosky},
journal= {arXiv preprint arXiv:math/9803078},
year = {2007}
}
Comments
145 pages In the revision a new chapter (chapter 6) has been added which proves a stronger local factorization Theorem. The introduction has also been modified. There are no other changes from the original March '98 submission