1 citations · 1 across the 13 of their papers we have counts for
19 papers
On the De Rham Cohomology of Zero-Dimensional Schemes
Martin Kreuzer, Le Ngoc Long
The (naive) de Rham cohomology of a zero-dimensional scheme is the homology of the Kähler differential algebra of its coordinate ring, viewed as a complex. Since it is well-known t…
The Canonical Exact Sequence of Differential Modules for 0-Dimensional Schemes
Tran N. K. Linh, Le Ngoc Long
Given a 0-dimensional scheme $\X$ in over a perfect field , we examine the second differential power of its homogeneous vanishing ideal. This enables us to esta…
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 …
Some line and conic arrangements and their Waldschmidt constants
Dinh Tuan Huynh, Tran N. K. Linh, Le Ngoc Long
We study the Waldschmidt constant of some configurations in the projective plane. In the first part, we show that the Waldschmidt constant of a set of points where…
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…
Optimal Re-Embeddings of Border Basis Schemes
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Border basis schemes are open subschemes of Hilbert schemes parametrizing 0-dimensional subschemes of of given length. They yield open coverings and are easy to desc…
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…
The Kähler Different of a Set of Points in
Tran N. K. Linh, Le N. Long, Nguyen T. Hoa +2
Given an ACM set of points in a multiprojective space over a field of characteristic zero, we are interested in studying the Kähler di…
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…
Hilbert Polynomials of Kähler Differential Modules for Fat Point Schemes
Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long
Given a fat point scheme in the projective -space over a field of characteristic zero, the modules of Kähler differential $k…
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…
On the Dedekind different of a Cayley-Bacharach scheme
Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long
Given a 0-dimensional scheme in a projective space over a field , we characterize the Cayley-Bacharach property of in terms of the alg…
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…
Kaehler differentials for fat point schemes in P^1xP^1
Elena Guardo, Martin Kreuzer, Tran N. K. Linh +1
Let be a set of -rational points in over a field of characteristic zero, let be a fat point scheme supported at , and let be the bihomogen…