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Title Abelian Arrangements
URL
Publication Date
Date Accessioned
Degree PhD
Discipline/Department Department of Mathematics
Degree Level doctoral
University/Publisher University of Oregon
Abstract An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. We are interested in the topology of the complement of an arrangement. If the arrangement is unimodular, we provide a combinatorial presentation for a differential graded algebra (DGA) that is a model for the complement, in the sense of rational homotopy theory. Moreover, this DGA has a bi-grading that allows us to compute the mixed Hodge numbers. If the arrangement is chordal, then this model is a Koszul algebra. In this case, studying its quadratic dual gives a combinatorial description of the Q-nilpotent completion of the fundamental group and the minimal model of the complement of the arrangement. This dissertation includes previously unpublished co-authored material.
Subjects/Keywords Hyperplane arrangements
Contributors Proudfoot, Nicholas (advisor)
Language en
Rights All Rights Reserved.
Country of Publication us
Record ID handle:1794/19273
Repository oregon
Date Retrieved
Date Indexed 2020-06-18
Grantor University of Oregon
Issued Date 2015-08-18 00:00:00

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