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Efficiently Checking Separating Indeterminates
Bernhard Andraschko, Martin Kreuzer, Le Ngoc Long
In this paper we continue the development of a new technique for computing elimination ideals by substitution which has been called -separating re-embeddings. Given an ideal …
Re-embeddings of Affine Algebras Via Gröbner Fans of Linear Ideals
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Given an affine algebra over a field , where is an ideal in the polynomial ring , we examine the task of effectively calculating r…
Differential theory of zero-dimensional schemes
Martin Kreuzer, Tran N. K. Linh, Le N. Long
For a 0-dimensional scheme in over a perfect field , we first embed the homogeneous coordinate ring into its truncated integral closure $\widetil…
The Kähler different of a 0-dimensional scheme
Le Ngoc Long
Given a 0-dimensional scheme in the projective -space over a field , we are interested in studying the Kähler different of and its…
Restricted Gröbner fans and re-embeddings of affine algebras
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
In this paper we continue the study of good re-embeddings of affine K-algebras started in [KLR]. The idea is to use special linear projections to find isomorphisms between a given…
Cotangent spaces and separating re-embeddings
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Given an affine algebra , where is a polynomial ring over a field and is an ideal in , we study re-embeddings of the affine scheme ${\rm Spec…
Computing subschemes of the border basis scheme
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
A good way of parametrizing 0-dimensional schemes in an affine space has been developed in the last 20 years using border basis schemes. Given a multiplicity ,…
An application of Liaison theory to zero-dimensional schemes
Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long +1
Given a 0-dimensional scheme X in a n-dimensional projective space P^n_K over an arbitrary field K, we use Liaison theory to characterize the Cayley-Bacharach property of X. Our re…
Algorithms for Checking Zero-Dimensional Complete Intersections
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Given a 0-dimensional affine K-algebra R=K[x_1,...,x_n]/I, where I is an ideal in a polynomial ring K[x_1,...,x_n] over a field K, or, equivalently, given a 0-dimensional affine sc…
On the Cayley-Bacharach Property
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
The Cayley-Bacharach property, which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional af…
Kähler differential algebras for 0-dimensional schemes
Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long
Given a 0-dimensional scheme in a projective space over a field , we study the Kähler differential algebra of its homogeneous coordinate ring . Using…