GKZ Systems and Hyperplane Arrangements

The purpose of the project is to find relationships between two families of DE which arise from hyperplane arrangements - GKZ (Gelfand-Kapranov-Zelevinsky) Systems and Gauss-Manin Connections. We begin by outlining the fundamentals of both approaches and highlight the basics of D-modules, the machinery used to link the two together. What follows are several investigations: the case of n points in the complex line, an example of two different arrangements which yield isomorphic GKZ systems and a generalization due to C.Bremer, and, finally, presentations of the cases of 4, 5, and 6 lines in the complex plane.