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Full-Text Articles in Discrete Mathematics and Combinatorics
Distribution Of The P-Torsion Of Jacobian Groups Of Regular Matroids, Sergio R. Zapata Ceballos
Distribution Of The P-Torsion Of Jacobian Groups Of Regular Matroids, Sergio R. Zapata Ceballos
Electronic Thesis and Dissertation Repository
Given a regular matroid $M$ and a map $\lambda\colon E(M)\to \N$, we construct a regular matroid $M_\lambda$. Then we study the distribution of the $p$-torsion of the Jacobian groups of the family $\{M_\lambda\}_{\lambda\in\N^{E(M)}}$. We approach the problem by parameterizing the Jacobian groups of this family with non-trivial $p$-torsion by the $\F_p$-rational points of the configuration hypersurface associated to $M$. In this way, we reduce the problem to counting points over finite fields. As a result, we obtain a closed formula for the proportion of these groups with non-trivial $p$-torsion as well as some estimates. In addition, we show that the …
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 …