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Cohomology of abelian arrangements


Author: Christin Bibby
Journal: Proc. Amer. Math. Soc. 144 (2016), 3093-3104
MSC (2010): Primary 52C35; Secondary 14F99, 55T99
DOI: https://doi.org/10.1090/proc/12937
Published electronically: November 20, 2015
MathSciNet review: 3487239
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Abstract: An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. In this paper, we study the cohomology of the complement of an abelian arrangement. For unimodular abelian arrangements, we provide a combinatorial presentation for a differential graded algebra whose cohomology is isomorphic to the rational cohomology of the complement. Moreover, this DGA has a bi-grading that allows us to compute the mixed Hodge numbers.


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Additional Information

Christin Bibby
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Address at time of publication: Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7
Email: cbibby2@uwo.ca

DOI: https://doi.org/10.1090/proc/12937
Received by editor(s): June 7, 2015
Received by editor(s) in revised form: August 11, 2015
Published electronically: November 20, 2015
Additional Notes: This research was partially supported by NSF grant DMS-0950383.
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2015 American Mathematical Society