The broken circuit complex and the Orlik - Terao algebra of a hyperplane arrangement

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Title: The broken circuit complex and the Orlik - Terao algebra of a hyperplane arrangement
Authors: Le, Van Dinh
Thesis advisor: Prof. Dr. Tim Römer
Thesis referee: Prof. Dr. Hal Schenck
Abstract: My thesis is mostly concerned with algebraic and combinatorial aspects of the theory of hyperplane arrangements. More specifically, I study the Orlik-Terao algebra of a hyperplane arrangement and the broken circuit complex of a matroid. The Orlik-Terao algebra is a useful tool for studying hyperplane arrangements, especially for characterizing some non-combinatorial properties. The broken circuit complex, on the one hand, is closely related to the Orlik-Terao algebra, and on the other hand, plays a crucial role in the study of many combinatorial problem: the coefficients of the characteristic polynomial of a matroid are encoded in the f-vector of the broken circuit complex of the matroid. Among main results of the thesis are characterizations of the complete intersection and Gorenstein properties of the broken circuit complex and the Orlik-Terao algebra. I also study the h-vector of the broken circuit complex of a series-parallel network and relate certain entries of that vector to ear decompositions of the network. An application of the Orlik-Terao algebra in studying the relation space of a hyperplane arrangement is also included in the thesis.
URL: https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016021714257
Subject Keywords: Broken circuit complex; Hyperplane arrangement; Orlik - Terao algebra; h-vector; Relation space; Complete intersection; Gorenstein; Linear resolution; Series - parallel network; Matroid
Issue Date: 17-Feb-2016
License name: Namensnennung 3.0 Unported
License url: http://creativecommons.org/licenses/by/3.0/
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

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