Tom BradenLin, Shuo2024-04-262024-04-262023-092023-0910.7275/35952790https://hdl.handle.net/20.500.14394/19406In this thesis we study the intersection cohomology of arrangement Schubert varieties with coefficients in a rank one local system on a hyperplane arrangement complement. We prove that the intersection cohomology can be computed recursively in terms of certain polynomials, if a local system has only $\pm 1$ monodromies. In the case where the hyperplane arrangement is generic central or equivalently the associated matroid is uniform and the local system has only $\pm 1$ monodromies, we prove that the intersection cohomology is a combinatorial invariant. In particular when the hyperplane arrangement is associated to the uniform matroid of rank $n-1$ over $n$ elements, and the local system has $\pm 1$ monodromies, we can give a closed formula for the intersection cohomology.hyperplane arrangementintersection cohomologylocal systemmatroidAlgebraic GeometryDiscrete Mathematics and CombinatoricsGeometry and TopologyDissertation (Open Access)https://orcid.org/0009-0004-6263-9296