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.
Copyright 2012 Erik Andrew Insko
Insko, Erik Andrew. "Equivariant cohomology and local invariants of Hessenberg varieties." dissertation, University of Iowa, 2012.