70,138 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
Cohen-Macaulay Properties of Square-Free Monomial Ideals
In this paper we study simplicial complexes as higher dimensional graphs in
order to produce algebraic statements about their facet ideals. We introduce a
large class of square-free monomial ideals with Cohen-Macaulay quotients, and a
criterion for the Cohen-Macaulayness of facet ideals of simplicial trees. Along
the way, we generalize several concepts from graph theory to simplicial
complexes.Comment: 28 pages, 17 figure
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