@Article{CMR-40-154, author = {Xu , Jiajun and Zhang , Guanglian}, title = {Symplectic Conditions on Grassmannian, Flag, and Schubert Varieties}, journal = {Communications in Mathematical Research }, year = {2024}, volume = {40}, number = {2}, pages = {154--190}, abstract = {

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├╝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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0034}, url = {http://global-sci.org/intro/article_detail/cmr/23086.html} }