共查询到20条相似文献,搜索用时 10 毫秒
1.
Marcin Dumnicki Brian Harbourne Tomasz Szemberg Halszka Tutaj-Gasińska 《Advances in Mathematics》2014
Inspired by results of Guardo, Van Tuyl and the second author for lines in P3, we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r -dimensional planes in Pn for n?2r+1. These considerations lead to new conjectures that suggest that the well known conjecture of Nagata for points in P2 is not an exotic statement but rather a manifestation of a much more general phenomenon which seems to have been overlooked so far. 相似文献
2.
Let S be a polynomial ring and I be the Stanley-Reisner ideal of a simplicial complex Δ. The purpose of this paper is investigating the Buchsbaum property of S/I(r) when Δ is pure dimension 1. We shall characterize the Buchsbaumness of S/I(r) in terms of the graphical property of Δ. That is closely related to the characterization of the Cohen-Macaulayness of S/I(r) due to the first author and N.V. Trung. 相似文献
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Margherita Barile 《Archiv der Mathematik》2006,87(6):516-521
We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms
of the number of its minimal monomial generators and the maximum height of its minimal primes.
Received: 12 December 2005 相似文献
5.
This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gröbner basis can be computed by studying paths in the graph. Since these Gröbner bases are square-free, generalized binomial edge ideals are radical. To find the primary decomposition a combinatorial problem involving the connected components of subgraphs has to be solved. The irreducible components of the solution variety are all rational. 相似文献
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V. Bonanzinga 《Archiv der Mathematik》2003,81(4):385-396
In this paper we characterize all principal Borel ideals with Borel generator
up to degree 4 which are Gotzmann. We also classify principal Borel ideals with a
Borel generator of degree d which are lexsegment
and we describe the shadows of principal Borel ideals. Finally, we
discuss the corresponding results for squarefree monomial ideals.Received: 10 May 2002 相似文献
8.
Shiv Datt KumarSatya Mandal 《Journal of Pure and Applied Algebra》2002,169(1):29-32
We prove some results on projective generation of ideals. 相似文献
9.
We study the set of Cohen-Macaulay monomial ideals with a given radical. Among this set of ideals are the so-called Cohen-Macaulay modifications. Not all Cohen-Macaulay squarefree monomial ideals admit nontrivial Cohen-Macaulay modifications. It is shown that if there exists one such modification, then there exist indeed infinitely many. 相似文献
10.
Samuel Lundqvist 《Journal of Pure and Applied Algebra》2010,214(4):309-321
In this paper we discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give new complexity bounds. As an application, we drastically improve the computational algebra approach to the reverse engineering of gene regulatory networks. 相似文献
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Le Dinh Nam 《Journal of Pure and Applied Algebra》2011,215(6):1502-1515
In this paper, we use the tools of Gröbner bases and combinatorial secant varieties to study the determinantal ideals It of the extended Hankel matrices. Denote by c-chain a sequence a1,…,ak with ai+c<ai+1 for all i=1,…,k−1. Using the results of c-chain, we solve the membership problem for the symbolic powers and we compute the primary decomposition of the product It1?Itk of the determinantal ideals. Passing through the initial ideals and algebras we prove that the product It1?Itk has a linear resolution and the multi-homogeneous Rees algebra is defined by a Gröbner basis of quadrics. 相似文献
13.
We find a sufficient condition that is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function cannot be level if hd≤2d+3, and that there exists a level O-sequence of codimension 3 of type for hd≥2d+k for k≥4. Furthermore, we show that is not level if , and also prove that any codimension 3 Artinian graded algebra A=R/I cannot be level if . In this case, the Hilbert function of A does not have to satisfy the condition hd−1>hd=hd+1.Moreover, we show that every codimension n graded Artinian level algebra having the Weak-Lefschetz Property has a strictly unimodal Hilbert function having a growth condition on (hd−1−hd)≤(n−1)(hd−hd+1) for every d>θ where
h0<h1<<hα==hθ>>hs−1>hs.