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Koszulness and supersolvability for Dirichlet arrangements


Author: Bob Lutz
Journal: Proc. Amer. Math. Soc. 147 (2019), 4937-4947
MSC (2010): Primary 52C35; Secondary 05B35, 16S37
DOI: https://doi.org/10.1090/proc/14591
Published electronically: July 30, 2019
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Abstract:

We prove that the cone over a Dirichlet arrangement is supersolvable if and only if its Orlik-Solomon algebra is Koszul. This was previously shown for four other classes of arrangements. We exhibit an infinite family of cones over Dirichlet arrangements that are combinatorially distinct from these other four classes.


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Additional Information

Bob Lutz
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: boblutz@umich.edu

DOI: https://doi.org/10.1090/proc/14591
Received by editor(s): May 12, 2018
Received by editor(s) in revised form: August 23, 2018, and December 23, 2018
Published electronically: July 30, 2019
Additional Notes: Work of the author was partially supported by NSF grants DMS-1401224 and DMS-1701576.
Communicated by: Patricia Hersh
Article copyright: © Copyright 2019 American Mathematical Society