Date of Degree
PhD (Doctor of Philosophy)
Julianna S. Tymoczko
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.
Equivariant cohomology, Hessenberg varieties, Singular loci
vi, 113 pages
Includes bibliographical references (pages 108-113).
Copyright 2012 Erik Andrew Insko