Strong Toroidalization of Dominant Morphisms of 3-folds

2006/01/03 by Steven Dale Cutkosky, Cutkosky, Steven Dale
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0601037

Abstract

Suppose that f:X→ Y is a dominant morphism of 3-folds over an algebraically closed field of characteristic zero. We prove that there exist sequences of blow ups of points and nonsingular curves Φ:X₁→ X and Ψ:Y₁→ Y such that the induced map f₁:Y₁→ X₁ is a toroidal morphism. This extends an earlier proof of the author of this theorem with the extra assumption that f is birational.

Related

• Toroidalization of birational morphisms of 3-folds
• Strong Toroidalization of Birational Morphisms of 3-Folds
• A simpler proof of toroidalization of morphisms from 3-folds to surfaces
• Weak toroidalization over non-closed fields
• Monomialization of Morphisms From 3 Folds to Surfaces