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 is much more complicated.
On présente une démonstration plus simple et plus conceptuelle de la toroïdalisation des morphismes des variétés de dimension trois vers les surfaces, sur un corps algébriquement clos de caractéristique zéro. On obtient la toroïdalisation par une série d’éclatements de sous-variétés non singulières au-dessus de la source et de l’image, afin d’obtenir un morphisme torique. La démonstration originale de la toroïdalisation des morphismes des variétés de dimension trois vers les surfaces était beaucoup compliquée.
Keywords: Morphism, toroidalization, monomialization
Mot clés : Morphisme, toroidalisation, monomialisation
@article{AIF_2013__63_3_865_0, author = {Cutkosky, Steven Dale}, title = {A simpler proof of toroidalization of morphisms from 3-folds to surfaces}, journal = {Annales de l'Institut Fourier}, pages = {865--922}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {63}, number = {3}, year = {2013}, doi = {10.5802/aif.2779}, zbl = {1282.14029}, mrnumber = {3137475}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2779/} }
TY - JOUR AU - Cutkosky, Steven Dale TI - A simpler proof of toroidalization of morphisms from 3-folds to surfaces JO - Annales de l'Institut Fourier PY - 2013 SP - 865 EP - 922 VL - 63 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2779/ DO - 10.5802/aif.2779 LA - en ID - AIF_2013__63_3_865_0 ER -
%0 Journal Article %A Cutkosky, Steven Dale %T A simpler proof of toroidalization of morphisms from 3-folds to surfaces %J Annales de l'Institut Fourier %D 2013 %P 865-922 %V 63 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2779/ %R 10.5802/aif.2779 %G en %F AIF_2013__63_3_865_0
Cutkosky, Steven Dale. A simpler proof of toroidalization of morphisms from 3-folds to surfaces. Annales de l'Institut Fourier, Volume 63 (2013) no. 3, pp. 865-922. doi : 10.5802/aif.2779. http://www.numdam.org/articles/10.5802/aif.2779/
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