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Characteristic Polynomial Of Arrangements And Multiarrangements, Mehdi Garrousian
Characteristic Polynomial Of Arrangements And Multiarrangements, Mehdi Garrousian
Electronic Thesis and Dissertation Repository
This thesis is on algebraic and algebraic geometry aspects of complex hyperplane arrangements and multiarrangements. We start by examining the basic properties of the logarithmic modules of all orders such as their freeness, the cdga structure, the local properties and close the first chapter with a multiarrangement version of a theorem due to M. Mustata and H. Schenck.
In the next chapter, we obtain long exact sequences of the logarithmic modules of an arrangement and its deletion-restriction under the tame conditions. We observe how the tame conditions transfer between an arrangement and its deletion-restriction.
In chapter 3, we use some …
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 …