Formal desingularization of surfaces: The Jung method revisited

  • Authors:

  • Tobias Beck

  • Affiliations:

  • Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraβe 69, A-4020 Linz, Austria

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2009

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Abstract

In this paper we propose the concept of formal desingularizations as a substitute for the resolution of algebraic varieties. Though a usual resolution of algebraic varieties provides more information on the structure of singularities there is evidence that the weaker concept is enough for many computational purposes. We give a detailed study of the Jung method and show how it facilitates an efficient computation of formal desingularizations for projective surfaces over a field of characteristic zero, not necessarily algebraically closed. The paper includes a constructive extension of the Theorem of Jung-Abhyankar, a generalization of Duval's Theorem on rational Puiseux parametrizations to the multivariate case and a detailed description of a system for multivariate algebraic power series computations.