A simpler proof of toroidalization of morphisms from 3-folds to surfaces  [ Une démonstration plus simple de la toroïdalisation des morphismes des variétés de dimension trois vers les surfaces ]
Annales de l'Institut Fourier, Tome 63 (2013) no. 3, pp. 865-922.

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.

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.

DOI : https://doi.org/10.5802/aif.2779
Classification : 14E99,  14E15
Mots 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'institut Fourier},
     volume = {63},
     number = {3},
     year = {2013},
     doi = {10.5802/aif.2779},
     mrnumber = {3137475},
     zbl = {1282.14029},
     language = {en},
     url = {www.numdam.org/item/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, Tome 63 (2013) no. 3, pp. 865-922. doi : 10.5802/aif.2779. http://www.numdam.org/item/AIF_2013__63_3_865_0/

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