Monomialization of Morphisms From 3 Folds to Surfaces

2000/10/01 by Steven Dale Cutkosky, Cutkosky, Steven Dale
Mathematics · #14E #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E

paper · pdf · doi:10.48550/arxiv.math/0010002

192 pages

arxiv created 2000/10/01 · arxiv updated 2009/11/30

Abstract

Suppose that Φ:X→ Y is a morphism from a 3 fold to a surface (over an algebraically closed field of characteristic zero). We prove that there exist sequences of blowups of nonsingular subvarieties X₁→ X and Y₁→ Y such that the morphism Φ₁:X₁→ Y₁ is a ``Monomial Morphism''. As a corollary, we show that we can make Φ₁ a toroidal morphism.

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