论文标题
典型的希尔伯特·比奇（Hilbert-Burch）电力系列
Canonical Hilbert-Burch matrices for power series
论文作者
论文摘要
在多项式环$ K [x，y] $中，相对于给定术语排序共享相同领先术语理想的零维理想集已知是称为gröbner细胞的仿射空间。 Conca-valla和Constantinescu分别以某些规范的Hilbert-Burch矩阵分别用于词典和度量学术语订单的某些规范的Hilbert-Burch矩阵。 在本文中，我们给出了$（x，y）$ - Gröbner细胞中的主要理想的参数化，该理想与此类理想的局部结构兼容。更准确地说，我们通过定义了功率系列环$ k [[x，y]] $在本地术语订购中的零维理想$ k [[x，y] $中的零维理想中的规范希尔伯特 - 养蜂矩阵的概念。
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 Gröbner cells. Conca-Valla and Constantinescu parametrize such Gröbner cells 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 Gröbner 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.
