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On Rings Of Invariants For Cyclic P-Groups, Daniel Juda
On Rings Of Invariants For Cyclic P-Groups, Daniel Juda
Graduate Theses and Dissertations
This thesis studies the ring of invariants R^G of a cyclic p-group G acting on k[x_1,\ldots, x_n] where k is a field of characteristic p >0. We consider when R^G is Cohen-Macaulay and give an explicit computation of the depth of R^G. Using representation theory and a result of Nakajima, we demonstrate that R^G is a unique factorization domain and consequently quasi-Gorenstein. We answer the question of when R^G is F-rational and when R^G is F-regular.
We also study the a-invariant for a graded ring S, that is, the maximal graded degree of the top local cohomology module of S. …