Efficient desingularization of reducible algebraic sets

ABSTRACT

In this paper we present a resolution strategy that uses a modification of Villamayor's algorithm as a subroutine and combines resolutions of irreducible (or at least equidimensional) components of a given algebraic set X⊂ W to compute an embedded resolution of singularities of X. The arising algorithm extends the scope of Villamayor's algorithm from equidimensional algebraic sets to the general case. The ideas also serve well in improving the efficiency of resolutions, using the prime ideal decomposition of the (radical) vanishing ideal of X

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms

General Terms:
Theory

Keywords:
blowups, embedded resolution of singularities, normal crossings