Formal Desingularization of Surfaces - The Jung Method Revisited -

Details Formal Desingularization of Surfaces - The Jung Method Revisited - Formal Desingularization of Surfaces - The Jung Method Revisited -

2008-01-15

arxiv.org/abs/0801.2282v1

Mathematics

Algebraic Geometry

33 pages, 2 figures

Scientific paper

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 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.

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