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TitleFormal desingularization of surfaces: The Jung method revisited
Author(s) Thomas Becker
TypeArticle in Journal
AbstractIn 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.
KeywordsResolution of singularities, Algebraic power series, Quasi-ordinary polynomials
URL http://www.sciencedirect.com/science/article/pii/S0747717108001028
JournalJournal of Symbolic Computation
Pages131 - 160
Translation No
Refereed No