Geometriae Dedicata

, Volume 163, Issue 1, pp 61–103 | Cite as

Simultaneous algorithmic resolution of singularities

Original Paper
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Abstract

This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic zero. The paper’s approach is more indirect: it primarily considers the more general case of families of basic objects (or marked ideals). A definition of algorithmic equiresolution is proposed, which applies to families whose parameter space T may be non-reduced, e.g., the spectrum of a suitable artinian ring. Other definitions of algorithmic equiresolution are also discussed. These are geometrically very natural, but the parameter space T of the family must be assumed regular. It is proven that when T is regular all the proposed definitions are equivalent.

Keywords

Resolution algorithm Embedded variety Coherent ideal Basic object 

Mathematics Subject Classification

14B05 14E15 14F05 14D99 
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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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