Let R be a Noetherian ring and I an ideal in R. Then there exists an integer k such that for all n 1 there exists a primary decomposition I n = q 1 \ \ q s such that for all i, p q i nk q i. Also, for each homogeneous ideal I in a polynomial ring over a eld there exists an integer k such that the Castelnuovo-Mumford regularity of I n is bounded above by kn. The regularity part follows from the ...

The problem of computing a minimal set of generators for the ideal of a rational parametric projective curve has been tackled by elimination theory and can be solved by the computation of Gröbner bases (see, for example Kalkbrener, 1991; Licciardi and Mora, 1994; Gao and Chou, 1992; Fix et al., 1996, and references therein). These methods have been implemented in CoCoA 3.6 (Capani et al., 1995)...

Introduction. The aim of this article is to show how one may use interesting properties of the canonical module for computational applications. It seems that the ideas we develop here are not used in computational algebraic geometry today. We do not claim any major improvement on the theoretical complexity of the problems we address, however we have the feeling that this alternative approach fo...

Suppose S is a parametrized surface in complex projective 3-space P given as the image of φ : P ×P1 → P. The implicitization problem is to compute an implicit equation F = 0 of S using the parametrization φ. An algorithm using syzygies exists for computing F if φ has no base points, i.e. φ is everywhere defined. This work is an extension of this algorithm to the case of a surface with multiple ...

In numerical algebraic geometry, a witness point set W is a key object for performing numerical computations on a projective scheme X of pure dimension d > 0 defined over C. If X is arithmetically Cohen-Macaulay, W can also be used to obtain information about X, such as the initial degree of the ideal generated by X and its Castelnuovo-Mumford regularity. Due to this relationship, we develop a ...