Theses and Dissertations from UMD

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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

More information is available at Theses and Dissertations at University of Maryland Libraries.

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    Matroids and Geometric Invariant Theory of torus actions on flag spaces
    (2006-04-06) Howard, Benjamin James; Millson, John J; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This thesis investigates the structure of the projective coordinate rings of SL(n,C) weight varieties. An SL(n,C) weight variety is a Geometric Invariant Theory quotient of the space of full flags by the maximal torus in SL(n,C). Special cases include configurations of n-tuples of points in projective space modulo automorphisms of projective space. There are three main results. The first is an explicit finite set of generators for the coordinate ring. The second is that the lowest degree elements of the coordinate ring provide a well-defined map from the weight variety to projective space. The third theorem is an explicit presentation for the ring of projective invariants of n ordered points on the Riemann sphere, in the case that each point is weighted by an even integer. The methods applied involve matroid theory and degenerations of the weight varieties to toric varieties attached to Gelfand Tsetlin polytopes.