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). / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/28478 |
| Date | January 2023 |
| Creators | Atar, Busra |
| Contributors | Harada, Megumi, Rajchgot, Jenna, Mathematics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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