Open Access
Translator Disclaimer
June 2011 Some natural properties of constructive resolution of singularities
Angélica Benita, Santiago Encinas, Orlando E. Villamayor U.
Asian J. Math. 15(2): 141-192 (June 2011).


These expository notes, addressed to non-experts, are intended to present some of Hironaka’s ideas on his theorem of resolution of singularities. We focus particularly on those aspects which have played a central role in the constructive proof of this theorem.

In fact, algorithmic proofs of the theorem of resolution grow, to a large extend, from the so called Hironaka’s fundamental invariant. Here we underline the influence of this invariant in the proofs of the natural properties of constructive resolution, such as: equivariance, compatibility with open restrictions, with pull-backs by smooth morphisms, with changes of the base field, independence of the embedding, etc.


Download Citation

Angélica Benita. Santiago Encinas. Orlando E. Villamayor U.. "Some natural properties of constructive resolution of singularities." Asian J. Math. 15 (2) 141 - 192, June 2011.


Published: June 2011
First available in Project Euclid: 28 February 2012

zbMATH: 1239.14005
MathSciNet: MR2838219

Primary: 14E15

Keywords: Equivariance , log-principalization , resolution of singularities , singularities

Rights: Copyright © 2011 International Press of Boston


Vol.15 • No. 2 • June 2011
Back to Top