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Gkm Theory Of Rationally Smooth Group Embeddings, Richard P. Gonzales
Gkm Theory Of Rationally Smooth Group Embeddings, Richard P. Gonzales
Electronic Thesis and Dissertation Repository
This thesis is concerned with the study of rationally smooth group embeddings. We prove that the equivariant cohomology of any of these compactifications
can be described, via GKM-theory, as certain ring of piecewise polynomial functions.
Moreover, building on previous work of Renner, we show that the embeddings under consideration come equipped with both a canonical decomposition into rational cells and a filtration by equivariantly formal closed subvarieties.
The techniques developed in this monograph supply a method for constructing free
module generators on the equivariant cohomology of Q-filtrable GKM-varieties.
Our findings extend the earlier work of Arabia and Guillemin-Kogan on equivariant …
Descent Systems, Eulerian Polynomials And Toric Varieties, Letitia Mihaela Golubitsky
Descent Systems, Eulerian Polynomials And Toric Varieties, Letitia Mihaela Golubitsky
Electronic Thesis and Dissertation Repository
It is well-known that the Eulerian polynomials, which count permutations in S_n by their number of descents, give the h-polynomial/h-vector of the simple polytopes known as permutohedra, the convex hull of the Sn -orbit for a generic weight in the weight lattice of Sn . Therefore the Eulerian polynomials give the Betti numbers for certain smooth toric varieties associated with the permutohedra. In this thesis we derive recurrences for the h-vectors of a family of polytopes generalizing this. The simple polytopes we consider arise as the orbit of a non-generic weight, namely a weight fixed by only the simple reflections …