Abelian Arrangements

dc.contributor.advisor	Proudfoot, Nicholas
dc.contributor.author	Bibby, Christin
dc.date.accessioned	2015-08-18T23:04:51Z
dc.date.available	2015-08-18T23:04:51Z
dc.date.issued	2015-08-18
dc.description.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 This dissertation includes previously unpublished co-authored material.	en_US
dc.identifier.uri	https://hdl.handle.net/1794/19273
dc.language.iso	en_US
dc.publisher	University of Oregon
dc.rights	All Rights Reserved.
dc.subject	Hyperplane arrangements	en_US
dc.title	Abelian Arrangements
dc.type	Electronic Thesis or Dissertation
thesis.degree.discipline	Department of Mathematics
thesis.degree.grantor	University of Oregon
thesis.degree.level	doctoral
thesis.degree.name	Ph.D.

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