论文标题
格拉斯曼尼亚，国旗和舒伯特品种的符号条件
Symplectic conditions on Grassmannian, flag, and Schubert varieties
论文作者
论文摘要
在本文中，对相应（A型）代数品种中的符号（C型）格拉曼尼亚/国旗/舒伯特品种的定义定义方程的描述作为线性多项式在PL $ \ ddot {u} $ cker坐标中，并且在类型中产生了类型的应用程序，将其作为线性多项式，并在此类型中产生类型的应用。从舒伯特（Schubert）型A型舒伯特（Schubert）品种获取舒伯特（Schubert）型的舒伯特（Schubert）种类所需的局部方程数量是计算的，并且在完整的交集方面给出了舒伯特（Schubert）类型C种类的进一步的几何特性。最后，讨论了舒伯特品种在非微调或cominuscule grassmannian中的平滑度，在同一类型的代数品种的研究中填补了差距。
In this paper, a description of the set-theoretical defining equations of symplectic (type C) Grassmannian/flag/Schubert varieties in corresponding (type A) algebraic varieties is given as linear polynomials in Pl$\ddot{u}$cker coordinates, and it is proved that such equations generate the defining ideal of variety of type C in those of type A. As applications of this result, the number of local equations required to obtain the Schubert variety of type C from the Schubert variety of type A is computed, and further geometric properties of the Schubert variety of type C are given in the aspect of complete intersections. Finally, the smoothness of Schubert variety in the non-minuscule or cominuscule Grassmannian of type C is discussed, filling gaps in the study of algebraic varieties of the same type.
