Details:
Title  A modified coefficient ideal for use with the strict transform  Author(s)  Anne FrühbisKrüger  Type  Article in Journal  Abstract  Two main algorithmic approaches are known for making Hironaka’s proof of resolution of singularities in characteristic zero constructive. Their main differences are the use of different notions of transforms during the resolution process and the different use of exceptional divisors in the descent in ambient dimension. In this article, we focus on the first difference. Only the approach using the weak transform has up until now been successfully used in implementations, because the other one requires an explicit stratification by the Hilbert–Samuel function at each step of the algorithm which is highly impractical due to the high complexity of the computation of such a stratification. In this article, a (hybridtype) algorithmic approach is proposed which allows the use of the strict transform without the full impact of the complexity of the stratification by the Hilbert–Samuel function at each step of the desingularization process. This new approach is not intended to always be superior to the previously implemented one, instead it has its strengths precisely at the weak point of the other one and is thus a candidate to be joined with it by an appropriate heuristic.  Keywords  Resolution of singularities, Desingularization, Coefficient ideal, Strict transform, Weak transform  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717110001744 
Language  English  Journal  Journal of Symbolic Computation  Volume  46  Number  5  Pages  550  560  Year  2011  Note  Groebner Bases and Applications  Edition  0  Translation 
No  Refereed 
No 
