2003/06/18 by Pedro Daniel Gonzalez Perez, Pedro D. González Pérez, Perez, Pedro Daniel Gonzalez · 2 citations
Computer Science · Mathematics · #14E15 #14M25 #32S15 #32S45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14E15 #msc:14M25 #msc:32S15 #msc:32S45
paper · pdf · doi:10.48550/arxiv.math/0306270
To apear in Annales de l'Institut Fourier (Grenoble)
arxiv created 2003/06/18 · openalex publication_date 2003/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485-503. In the first procedure the singularity is embedded as hypersurface. In the second procedure, which is inspired by a work of Goldin and Teissier for plane curves (see Resolving singularities of plane analytic branches with one toric morphism,loc. cit., pages 315-340), we re-embed the singularity in an affine space of bigger dimension in such a way that one toric morphism provides its embedded resolution. We compare both procedures and we show that they coincide under suitable hypothesis.