Am application of Kempf complex to hyper-discriminant

[3-圈定义的对称群的偏序]我们在n次对称群S_n上定义了x ≤ y的偏序当且仅当y=a_1[三键]a_kx，其中i（y）=i（x）+2k其中a_1，[三键]，a_k是连续三个字母递增或递减的3-圈，i（*）是S_n中元素 * 的逆数，弱布鲁哈特秩序的类比考虑了在这种排序中偶对是否可与恒等式相比较。证明了所有映射1到n或n-1的n次偶置换都可与恒等式相比较。[The在幂零变换下稳定的子空间簇]设f：V → V是V=λ型向量空间V的幂零线性变换，即Jordan块的大小λ_1[大于或等于]λ_2[大于或等于][三键][大于或等于]λ_1。对于V的f-稳定子空间W，即f（W）<$W，W和V/W的类型是映射f的类型|w：W → W和fv/w：V/W → V/W。对于划分ν和μ，我们研究了集合S（λ，ν，μ）={W <$V;f（W）<$W，type W=ν，type V/W=μ}和S（λ，ν，μ）的Zebraki闭包X（λ，ν，μ）在V维子空间的Grassmanian中的奇异轨迹|ν|.我们证明了S（λ，ν，μ）是非奇异的，它的连通分支是有理簇;引入了类属向量，定义了X（λ，ν，μ）的不可约分支的类属点，其Plucker坐标可以很简单地表示它们的定义方程.本文明确地描述了X（λ，（d），μ）的仿射开集的坐标环具有余维为2的奇异轨迹.

[A partila order on the symmetric groups defined by 3-cycles] We define a partial order on the symmetric group S_n of degree n by x【less than or equal】y iff y=a_1【triple bond】a_kx with i(y)=i(x)+2k where a_1,【triple bond】, a_k are 3-cycles of increasing or decreasing consecutive three letters and i(*) is the nmber of inversions of the element * of S_n, on the analogy of the weak Bruhat Order. Whether an even parmutaion is comparable to the identity or not in this ordering is considered. It is shown that all of the even permutations of degree n which map 1 to n or n-1 are comparable to the identity.[The varieties of subspaces stable under a nilpotent transformation] Let f : V → V be a nilpotent linear transformation of a vector space V of type V=λ,i.e. the size of Jordan blocks λ_1【greater than or equal】λ_2【greater than or equal】【triple bond】【greater than or equal】λ_ι. For an f-stable subspace W of V,i.e. f(W) ⊂ W, the types of W and V/W are those of the maps f|w : W → W and fv/w : V/W → V/W induced by f, respectively. For partitions ν and μ we investigate the set S(λ,ν,μ)={W ⊂ V;f(W) ⊂ W,type W=ν,type V/W=μ} and the singular locus of the Zariski closure X(λ,ν,μ) of S(λ,ν,μ) in the grassmaniann of subspaces of V of dimension |ν|. We show that S(λ,ν,μ) is nonsingular and its connected components are rational varieties ; generic vectors are introduced, which define the generic points of the irreducible components of X(λ,ν,μ) whose Plucker coordinates are fairly simple to express their defining equations. We describe explicitly the coordinate ring of an affine openset of X(λ,(d),μ) with the singular locus of codimension two.