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

Steven Dale Cutkosky[1]

  • [1] Department of Mathematics University of Missouri, Columbia, MO 65211, USA

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 3, page 865-922
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Cutkosky, Steven Dale. "A simpler proof of toroidalization of morphisms from 3-folds to surfaces." Annales de l’institut Fourier 63.3 (2013): 865-922. <http://eudml.org/doc/275453>.

@article{Cutkosky2013,
abstract = {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.},
affiliation = {Department of Mathematics University of Missouri, Columbia, MO 65211, USA},
author = {Cutkosky, Steven Dale},
journal = {Annales de l’institut Fourier},
keywords = {Morphism; toroidalization; monomialization; morphism},
language = {eng},
number = {3},
pages = {865-922},
publisher = {Association des Annales de l’institut Fourier},
title = {A simpler proof of toroidalization of morphisms from 3-folds to surfaces},
url = {http://eudml.org/doc/275453},
volume = {63},
year = {2013},
}

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
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 3
SP - 865
EP - 922
AB - 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.
LA - eng
KW - Morphism; toroidalization; monomialization; morphism
UR - http://eudml.org/doc/275453
ER -

References

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