Filippini, S. A., Ni, X., Torres, J., and Weyman, J. (2024). Residual Intersections and Schubert Varieties. arXiv preprint arXiv:2411.13481v1.
This paper aims to demonstrate a pattern for defining opposite Schubert varieties in ADE types, where the defining ideals of certain pairs of these varieties arise from residual intersections.
The authors employ a representation-theoretic approach, utilizing concepts from commutative algebra, linkage theory, and the geometry of Schubert varieties. They leverage the properties of extremal Plücker coordinates, Demazure modules, and crystal graphs to analyze the defining ideals of Schubert varieties and their residual intersections.
The research establishes a novel connection between the algebraic structure of defining ideals and the geometric properties of Schubert varieties in ADE types. The identified pattern and the residual intersection property offer a new perspective on understanding the defining equations of these varieties.
This work contributes to the fields of algebraic geometry and representation theory by providing a deeper understanding of the structure and properties of Schubert varieties. The findings have implications for the study of linkage theory, residual intersections, and the geometry of homogeneous spaces.
The paper primarily focuses on ADE types and specific patterns of Schubert varieties. Further research could explore similar patterns and residual intersection properties in other Lie types or for more general families of Schubert varieties. Additionally, investigating the computational aspects and potential applications of these findings in areas such as computational algebraic geometry and representation theory would be valuable.
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by Sara Angela ... às arxiv.org 11-21-2024
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