Hilbert functions of points on Schubert varieties in orthogonal Grassmannians
Hilbert functions of points on Schubert varieties in orthogonal Grassmannians
复制标题
正交格拉斯曼函数中舒伯特簇上点的希尔伯特函数
DOI：
10.1007/s10801-009-0188-x
复制
发表时间：
2007
影响因子：
0.8
通讯作者：
Shyamashree Upadhyay
中科院分区：
文献类型：
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作者：
K. Raghavan;Shyamashree Upadhyay
给定一个正交格拉斯曼的舒伯特簇上的一个点，我们计算多重性，更一般的希尔伯特函数。我们首先将问题从几何转化为组合数学，应用标准单项式理论。由此产生的组合问题的解决方案形成了大部分的文件。这种方法已经遵循较早解决同样的问题，格拉斯曼和辛格拉斯曼。作为应用，我们提出了一个解释的多重性的数量不相交的格路的某种。一个更重要的应用，虽然它没有出现在这里，但在其他地方，是计算初始理想，关于某些方便的单项订单，切锥的理想舒伯特品种。采取舒伯特品种是一个特殊的种类和点是“单位陪集，”我们的问题专门一个关于Pfidian理想，在文献中存在通过不同方法的治疗。在文献中也有一个几何解决方案时，点是一个“通用的奇点。”
Given a point on a Schubert variety in an orthogonal Grassmannian, we compute the multiplicity, more generally the Hilbert function. We first translate the problem from geometry to combinatorics by applying standard monomial theory. The solution of the resulting combinatorial problem forms the bulk of the paper. This approach has been followed earlier to solve the same problem for Grassmannians and symplectic Grassmannians.As an application, we present an interpretation of the multiplicity as the number of non-intersecting lattice paths of a certain kind. A more important application, although it does not appear here but elsewhere, is to the computation of the initial ideal, with respect to certain convenient monomial orders, of the ideal of the tangent cone to the Schubert variety.Taking the Schubert variety to be of a special kind and the point to be the ‘identity coset,’ our problem specializes to one about Pfaffian ideals, treatments of which by different methods exist in the literature. Also available in the literature is a geometric solution when the point is a ‘generic singularity.’
DOI：
--
发表时间：
2008
期刊：
影响因子：
--
作者：
T.;Ohtsuka;Takeshi Ikeda;池田 岳;池田 岳
通讯作者：
池田 岳