2008/01/15 by Beck, T.
#14B20 (Secondary) #14E15 (Primary) #14Q10 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0801.2282
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.