Two Computational Techniques for Singularity Resolution

This paper presents two efficient computational techniques in algebraic geometry. The first one allows the elimination of redundancies in the representation of quasi-projective varieties by atlases of affine charts. The second simplifies the computations with exponentiated ideals by attaching rational weights to the generators, applying Hironaka’s theory of idealistic exponents. As the main application, we used these techniques to speed up Villamayor’s algorithm for resolving hypersurface singularities in any dimension.