Multinets in P^2 and P^3
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Date
2013-10-03
Authors
Bartz, Jeremiah
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
In this dissertation, a method for producing multinets from a net in P^3 is presented. Multinets play an important role in the study of resonance varieties of the complement of a complex hyperplane arrangement and very few examples are known. Implementing this method, numerous new and interesting examples of multinets are identified. These examples provide additional evidence supporting the conjecture of Pereira and Yuzvinsky that all multinets are degenerations of nets. Also, a complete description is given of proper weak multinets, a generalization of multinets.
Description
Keywords
Hyperplane arrangements, Multi-arrangements, Multinets, Nets, Pencil of plane curves, Resonance varieities