Document Type

Dissertation

Date of Degree

Summer 2010

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Richard Randell

Abstract

A recent result of Salvetti and Settepanella gives, for a complexified real arrangement, an explicit description of a minimal CW decomposition as well as an explicit algebraic complex which computes local system homology. We apply their techniques to discriminantal arrangements in two dimensional complex space and calculate the boundary maps which will give local system homology groups given any choice of local system. This calculation generalizes several known results; examples are given related to Milnor fibrations, solutions of KZ equations, and the LKB representation of the braid group.

Another algebraic object associated to a hyperplane arrangement is the module of derivations. We analyze the behavior of the derivation module for an affine arrangement over an infinite field and relate its derivation module to that of its cone. In the case of an arrangement fibration, we analyze the relationship between the derivation module of the total space arrangement and those of the base and fiber arrangements. In particular, subject to certain restrictions, we establish freeness of the total space arrangement given freeness of the base and fiber arrangements.

Keywords

derivation module, hyperplane arrangements, topology

Pages

iv, 54 pages

Bibliography

Includes bibliographical references (pages 53-54).

Copyright

Copyright 2010 Amanda C Hager

Included in

Mathematics Commons

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