Desingularization algorithms I. Role of exceptional divisors

By Edward Bierstone, Pierre D. Milman. 2002

49 citations recorded by the source corpus.

The article is about a "desingularization principle" common to various canonical desingularization algorithms in characteristic zero, and the roles played by the exceptional divisors in the underlying local construction. We compare algorithms of the authors and of Villamayor and his collaborators, distinguishing between the fundamental effect of the way the exceptional divisors are used, and different theorems obtained because of flexibility allowed in the choice of "input data". We show how the meaning of "invariance" of the desingularization invariant, and the efficiency of the algorithm depend on the notion of "equivalence" of collections of local data used in the inductive construction.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/44aa8bb07737b24d39817afe70c1d36027fc3a86

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Simple Hironaka resolution in characteristic zero (2004, background): “invariant. To make all the processes canonical and relate the objects induced by restrictions we either interpret the invariant in a canonical though quite technical way (so called “Hironaka trick”) or build a relevant canonical resolution datum ([9],[10],[ 11 ],[17],[23],[25],[34], [35],[36]).”
A Simplified Proof of Desingularization and Applications (2002, background): “During the eighties and nineties, the first constructive proofs of resolution of singularities appeared: [7], [34] (and [35]), [17] (see also [ 8 ]).”