Singularities in Geometry and Topology

Blanlœil, Vincent; Ohmoto, Toru

doi:10.4171/118

IRMA Lectures in Mathematics and Theoretical Physics

2012

DOI: 10.4171/118

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Singularities in Geometry and Topology

Vincent Blanlœil¹,

Toru Ohmoto²

Abstract: for their encouragement and comments about my thesis. Also I would like to thank to my family and friends for the motivation, help and the support.

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A modified coefficient ideal for use with the strict transform

Frühbis–Krüger¹

2011

Journal of Symbolic Computation

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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 to 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 (hybrid-type) 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.

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A modified coefficient ideal for use with the strict transform

Frühbis–Krüger¹

2011

Journal of Symbolic Computation

View full text Add to dashboard Cite

show abstract

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Singularities in Geometry and Topology

Abstract: for their encouragement and comments about my thesis. Also I would like to thank to my family and friends for the motivation, help and the support.

Cited by 1 publication

References 15 publications

A modified coefficient ideal for use with the strict transform

A modified coefficient ideal for use with the strict transform

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