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Author ORCID Identifier
https://orcid.org/0009-0004-6263-9296
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2023
Month Degree Awarded
September
First Advisor
Tom Braden
Subject Categories
Algebraic Geometry | Discrete Mathematics and Combinatorics | Geometry and Topology
Abstract
In 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.
DOI
https://doi.org/10.7275/35952790
Recommended Citation
Lin, Shuo, "Intersection Cohomology of Rank One Local Systems for Arrangement Schubert Varieties" (2023). Doctoral Dissertations. 3012.
https://doi.org/10.7275/35952790
https://scholarworks.umass.edu/dissertations_2/3012
Included in
Algebraic Geometry Commons, Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons