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Strong Toroidalization of Dominant Morphisms of 3-folds

Steven Dale Cutkosky
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Abstract

Suppose that $f:X\to Y$ 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 $Φ:X_1\to X$ and $Ψ:Y_1\to Y$ such that the induced map $f_1:Y_1\to X_1$ is a toroidal morphism. This extends an earlier proof of the author of this theorem with the extra assumption that $f$ is birational.

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Steven Dale Cutkosky. 2006-01-03. Strong Toroidalization of Dominant Morphisms of 3-folds. https://arxiv.org/abs/math/0601037

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