ترغب بنشر مسار تعليمي؟ اضغط هنا

Canonical Hilbert-Burch matrices for ideals of $k[x,y]$

216   0   0.0 ( 0 )
 نشر من قبل Conca Aldo
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

An Artinian ideal $I$ of $k[x,y]$ has many Hilbert-Burch matrices. We show that there is a canonical choice. As an application, we determine the dimension of certain affine Grobner cells and their Betti strata recovering results of Ellingsrud and Str{o}mme, Gottsche and Iarrobino.



قيم البحث

اقرأ أيضاً

153 - Roser Homs , Anna-Lena Winz 2020
Sets of zero-dimensional ideals in the polynomial ring $k[x,y]$ that share the same leading term ideal with respect to a given term ordering are known to be affine spaces called Grobner cells. Conca-Valla and Constantinescu parametrize such Grobner c ells in terms of certain canonical Hilbert-Burch matrices for the lexicographical and degree-lexicographical term orderings, respectively. In this paper, we give a parametrization of $(x,y)$-primary ideals in Grobner cells which is compatible with the local structure of such ideals. More precisely, we extend previous results to the local setting by defining a notion of canonical Hilbert-Burch matrices of zero-dimensional ideals in the power series ring $k[[x,y]]$ with a given leading term ideal with respect to a local term ordering.
Let k be an arbitrary field (of arbitrary characteristic) and let X = [x_{i,j}] be a generic m x n matrix of variables. Denote by I_2(X) the ideal in k[X] = k[x_{i,j}: i = 1, ..., m; j = 1, ..., n] generated by the 2 x 2 minors of X. We give a recurs ive formulation for the lengths of the k[X]-module k[X]/(I_2(X) + (x_{1,1}^q,..., x_{m,n}^q)) as q varies over all positive integers using Grobner basis. This is a generalized Hilbert-Kunz function, and our formulation proves that it is a polynomial function in q. We give closed forms for the cases when m is at most 2, %as well as the closed forms for some other special length functions. We apply our method to give closed forms for these Hilbert-Kunz functions for cases $m le 2$.
Let $G$ be a finite simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in the polynomial ring $S = K[x_1, ldots, x_n, y_1, ldots, y_n].$ In this article, we compute the Hilbert series of binomial edge ideal of decompo sable graphs in terms of Hilbert series of its indecomposable subgraphs. Also, we compute the Hilbert series of binomial edge ideal of join of two graphs and as a consequence we obtain the Hilbert series of complete $k$-partite graph, fan graph, multi-fan graph and wheel graph.
164 - Douglas A. Leonard 2012
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite fields relati ve to a local monomial ordering. A non-homogeneous version of the standard (homogeneous) Rees algebra is introduced as well.
We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the cones generate d by the Hilbert functions of all modules, all modules with bounded a-invariant, and all modules with bounded Castelnuovo-Mumford regularity. The first of these cones is infinite-dimensional and simplicial, the second is finite-dimensional but neither simplicial nor polyhedral, and the third is finite-dimensional and simplicial.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا