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Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

Year Degree Awarded

2016

Month Degree Awarded

February

First Advisor

Alexei Oblomkov

Subject Categories

Algebraic Geometry

Abstract

We develop algorithms for describing elements of the affine Springer fiber in type

A for certain 2 g(C[[t]]). For these , which are equivalued, integral, and regular,

it is known that the affine Springer fiber, X, has a paving by affines resulting from

the intersection of Schubert cells with X. Our description of the elements of Xallow

us to understand these affine spaces and write down explicit dimension formulae. We

also explore some closure relations between the affine spaces and begin to describe the

moment map for the both the regular and extended torus action.

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