133 research outputs found
Formal Desingularization of Surfaces - The Jung Method Revisited -
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.Comment: 33 pages, 2 figure
Matrix representations for toric parametrizations
In this paper we show that a surface in P^3 parametrized over a 2-dimensional
toric variety T can be represented by a matrix of linear syzygies if the base
points are finite in number and form locally a complete intersection. This
constitutes a direct generalization of the corresponding result over P^2
established in [BJ03] and [BC05]. Exploiting the sparse structure of the
parametrization, we obtain significantly smaller matrices than in the
homogeneous case and the method becomes applicable to parametrizations for
which it previously failed. We also treat the important case T = P^1 x P^1 in
detail and give numerous examples.Comment: 20 page
Covering of surfaces parametrized without projective base points
This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in "Sendra J.R., Sevilla D., Villarino C. Covering of surfaces parametrized without projective base points. Proc. ISSAC2014 ACM Press, pages 375-380, 2014,\ud
ISBN:978-1-4503-2501-1". http://dx.doi.org/10.1145/2608628.2608635We prove that every a ne rational surface, parametrized by means of an a ne rational parametrization without projective base points, can be covered by at most three parametrizations.\ud
Moreover, we give explicit formulas for computing the coverings. We provide two di erent approaches: either\ud
covering the surface with a surface parametrization plus a curve parametrization plus a point, or with the original parametrization plus two surface reparametrizations of it
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