Nilpotent Hessenberg varieties are a family of subvarieties of the flag variety, which include the Springer varieties, the Peterson variety, and the whole flag variety. In this thesis I give a geometric proof that the cohomology of the flag variety surjects onto the cohomology of the Peterson variety; I provide a combinatorial criterion for determing the singular loci of a large family of regular nilpotent Hessenberg varieties; and I describe the equivariant cohomology of any regular nilpotent Hessenberg variety whose cohomology is generated by its degree two classes.
| Identifer | oai:union.ndltd.org:uiowa.edu/oai:ir.uiowa.edu:etd-3373 |
| Date | 01 July 2012 |
| Creators | Insko, Erik Andrew |
| Contributors | Tymoczko, Julianna, 1975- |
| Publisher | University of Iowa |
| Source Sets | University of Iowa |
| Language | English |
| Detected Language | English |
| Type | dissertation |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | Copyright 2012 Erik Andrew Insko |
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