@Article{CMR-40-2,
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 = {<p style="text-align: justify;">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 Plücker 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.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2023-0034},
url = {https://global-sci.com/article/90979/symplectic-conditions-on-grassmannian-flag-and-schubert-varieties}
}