Title page for ETD etd-06232012-104447


Type of Document Dissertation
Author Russell, Amber
Author's Email Address aruss16@lsu.edu, amcarus@gmail.com
URN etd-06232012-104447
Title Graham's Variety and Perverse Sheaves on the Nilpotent Cone
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Achar, Pramod Committee Chair
Adkins, William Committee Member
Litherland, Richard Committee Member
Oxley, James Committee Member
Sage, Daniel Committee Member
Wilmot, Chester Dean's Representative
Keywords
  • graham's variety
  • nilpotent cone
  • perverse sheaves
Date of Defense 2012-04-30
Availability unrestricted
Abstract
In recent work, Graham has defined a variety which maps to the nilpotent cone, and which shares many properties with the Springer resolution. However, Graham's map is not an isomorphism over the principal orbit, and for type A in particular, its fibers have a nice relationship with the fundamental groups of the nilpotent orbits. The goal of this dissertation is to determine which simple perverse sheaves appear when the Decomposition Theorem for perverse sheaves is applied in Graham's setting for type A, and to begin to answer this question in the other types as well.

In Chapter 1, we give some motivation and a brief description of this project. Then, Chapter 2 is a summary of several background topics. In Chapter 3, we review Graham's construction of his variety. In Chapter 4, we use results of Tymozcko to study the fibers of Graham's map in type A. Chapter 5 contains the conclusions in the perverse sheaf setting, and lastly, Chapter 6 contains results pertaining to Graham's fibers in the other types.

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