1998/03/17 by Steven Dale Cutkosky, Cutkosky, Steven Dale · 3 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.AG #msc:13B #msc:14E
paper · pdf · doi:10.48550/arxiv.math/9803078
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
arxiv created 1998/04/14 · arxiv updated 2009/11/30
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.