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Algorithmic resolution of singularities. (English) Zbl 1101.14015
Lossen, Christoph (ed.) et al., Singularities and computer algebra. Selected papers of the conference, Kaiserslautern, Germany, October 18–20, 2004 on the occasion of Gert-Martin Greuel’s 60th birthday. Cambridge: Cambridge University Press (ISBN 0-521-68309-2/pbk). London Mathematical Society Lecture Note Series 324, 157-183 (2006).
Summary: Although the problem of the existence of a resolution of singularities in characteristic zero was already proved by Hironaka in the 1960s and although algorithmic proofs of it have been given independently by the groups of Bierstone and Milman and of Encinas and Villamayor in the early 1990s, the explicit construction of a resolution of singularities of a given variety is still a very complicated computational task. In this article, we would like to outline the algorithmic approach of Encinas and Villamayor and simultaneously discuss the practical problems connected to the task of implementing the algorithm.
For the entire collection see [Zbl 1086.14001].

MSC:
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14Q15 Computational aspects of higher-dimensional varieties
14B05 Singularities in algebraic geometry
32S45 Modifications; resolution of singularities (complex-analytic aspects)
Software:
SINGULAR
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