Document Type

Dissertation

Date of Degree

Summer 2012

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Julianna S. Tymoczko

Abstract

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.

Keywords

Equivariant cohomology, Hessenberg varieties, Singular loci

Pages

vi, 113 pages

Bibliography

Includes bibliographical references (pages 108-113).

Copyright

Copyright 2012 Erik Andrew Insko

Included in

Mathematics Commons

Share

COinS