A simpler proof of toroidalization of morphisms from 3-folds to surfaces

Steven Cutkosky
2013 Annales de l'Institut Fourier  
We give a simpler and more conceptual proof of toroidalization of morphisms of 3-folds to surfaces, over an algebraically closed field of characteristic zero. A toroidalization is obtained by performing sequences of blow ups of nonsingular subvarieties above the domain and range, to make a morphism toroidal. The original proof of toroidalization of morphisms of 3-folds to surfaces, which appeared in Springer Lecture Notes in Math. in 2002 [12], is much more complicated.
doi:10.5802/aif.2779 fatcat:wnasfiooojbe7gnxrahjj2mrpi