Cohomology of abelian arrangements
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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.References
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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
- MR Author ID: 1157407
- Email: cbibby2@uwo.ca
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3093-3104
- MSC (2010): Primary 52C35; Secondary 14F99, 55T99
- DOI: https://doi.org/10.1090/proc/12937
- MathSciNet review: 3487239