Formal desingularization of surfaces: The Jung method revisited

• Autores: Tobias Beck
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 2, 2009, págs. 131-160
• Idioma: inglés
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• Resumen

  • 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.