Year: 2024
Author: Jiajun Xu, Guanglian Zhang
Communications in Mathematical Research , Vol. 40 (2024), Iss. 2 : pp. 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 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2023-0034
Communications in Mathematical Research , Vol. 40 (2024), Iss. 2 : pp. 154–190
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: Grassmannian variety generalized flag variety Schubert variety Plücker embedding complete intersection.