Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/29753
Title: | Gröbner Geometry for Hessenberg Varieties |
Authors: | Cummings, Mike |
Advisor: | Rajchgot, Jenna |
Department: | Mathematics |
Keywords: | Hessenberg varieties;patch ideals;Gröbner bases;triangular complete intersections |
Publication Date: | 2024 |
Abstract: | We study Hessenberg varieties in type A via their local defining equations, called patch ideals. We focus on two main classes of Hessenberg varieties: those associated to a regular nilpotent operator and to those associated to a semisimple operator. In the setting of regular semisimple Hessenberg varieties, which are known to be smooth and irreducible, we determine that their patch ideals are triangular complete intersections, as defined by Da Silva and Harada. For semisimple Hessenberg varieties, we give a partial positive answer to a conjecture of Insko and Precup that a given family of set-theoretic local defining ideals are radical. A regular nilpotent Hessenberg Schubert cell is the intersection of a Schubert cell with a regular nilpotent Hessenberg variety. Following the work of the author with Da Silva, Harada, and Rajchgot, we construct an embedding of the regular nilpotent Hessenberg Schubert cells into the coordinate chart of the regular nilpotent Hessenberg variety corresponding to the longest-word permutation in Bruhat order. This allows us to use work of Da Silva and Harada to conclude that regular nilpotent Hessenberg Schubert cells are also local triangular complete intersections. |
URI: | http://hdl.handle.net/11375/29753 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Cummings_Michael_GA_2024April_MSc.pdf | 541.45 kB | Adobe PDF | View/Open |
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