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http://hdl.handle.net/11375/28478
Title: | Hessenberg Patch Ideals of Codimension 1 |
Authors: | Atar, Busra |
Advisor: | Harada, Megumi Rajchgot, Jenna |
Department: | Mathematics |
Keywords: | Hessenberg variety;Frobenius splitting;Regular nilpotent;Flag variety |
Publication Date: | 2023 |
Abstract: | A Hessenberg variety is a subvariety of the flag variety parametrized by two maps: a Hessenberg function on $[n]$ and a linear map on $\C^n$. We study regular nilpotent Hessenberg varieties in Lie type A by focusing on the Hessenberg function $h=(n-1,n,\ldots,n)$. We first state a formula for the $f^w_{n,1}$ which generates the local defining ideal $J_{w,h}$ for any $w\in\Ss_n$. Second, we prove that there exists a convenient monomial order so that $\lead(J_{w,h})$ is squarefree. As a consequence, we conclude that each codimension-1 regular nilpotent Hessenberg variety is locally Frobenius split (in positive characteristic). |
URI: | http://hdl.handle.net/11375/28478 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Atar_Busra_202304_MasterOfScienceThesis.pdf | 411.94 kB | Adobe PDF | View/Open |
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