Am application of Kempf complex to hyper-discriminant

Kempf 复合体在超判别中的应用

• 批准号: 14540035
• 负责人: MAEDA Takashi
• 金额: $ 0.7万
• 依托单位: University of the Ryukyus
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540035/
• 关键词: nil potent linear trans formation; Jordan canonical form; grassmann variety; Little wood-Richardson tableaux; nil potent matrix; Schubert cell; homogeneous space; singular set; Littlewood-Richardson盤; べき零行列; Scnubert多様体; 特異点集合; 双対多様体; プリュッカー埋

[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.

[由3个循环定义的对称组上的partila顺序]我们在x fy = a_1 [triple bond] a_kx的对称组s_n上定义了部分顺序A_1，A_K是3个循环或连续的三个字母，而S_n的ient *是Bruhat秩序的类比。在nilpotent转换下，n或n-1是稳定的子空间的同一性]，让f：v→v→v→v→v→v→v eλ_1[大于或相等]λ_2[大于或等于] [大于或等于] λ_ι。 /w→v/w分别为f诱导。 ν，v/w =μ}和zariski闭合x（λ，ν，μ）的奇异基因座（λ，ν，μ）（λ，ν，μ） s（λ，ν，μ）是非单调的ATS成分，是X（λ，ν，μ）的Fe不可还原分量； x（λ，（d）

项目成果

T.Maeda: "Determinantal equations and cingular loci of duals of grassmunnians"Ryukyu Math.J.. 14. 17-40 (2001)

T.Maeda：“格拉斯穆尼安对偶的行列式方程和扣带轨迹”Ryukyu Math.J.. 14. 17-40 (2001)

T.Maeda: "The varieties of subspaces stable under a mil potent transformation"Ryukyu Math.J.. 16. 43-71 (2003)

T.Maeda：“在米尔有效变换下稳定的子空间的变化”Ryukyu Math.J.. 16. 43-71 (2003)

T.Maeda: "A partial order on the symmetric groups defined by 3-cycles"Ryukyu Math.J.. 15. 19-42 (2001)

T.Maeda：“由 3 圈定义的对称群的偏序”Ryukyu Math.J.. 15. 19-42 (2001)

T.Maeda: "A partial order on the symmetric groups defined by 3-cycles"Ryukyu Math.J.. 15. 19-42 (2002)

T.Maeda：“由 3 圈定义的对称群的偏序”Ryukyu Math.J.. 15. 19-42 (2002)

T.Maeda: "The Varieties of subspaces stable under a nilpotent transformation"Ryukyu Math.J.. 16. 43-71 (2003)

T.Maeda：“幂零变换下稳定的子空间的多样性”Ryukyu Math.J.. 16. 43-71 (2003)