Symplectic Conditions on Grassmannian,Flag,and Schubert Varieties  

作　　者：Jiajun Xu Guanglian Zhang 

机构地区：[1]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China.

出　　处：《Communications in Mathematical Research》2024年第2期154-190,共37页数学研究通讯（英文版）

摘　　要：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 Plucker 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.

关 键 词：Grassmannian variety generalized flag variety Schubert variety Plucker embedding complete intersection. 

分 类 号：O411[理学—理论物理]