## Koszulness and supersolvability for Dirichlet arrangements

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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.## References

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## Additional Information

**Bob Lutz**- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- MR Author ID: 1053423
- Email: boblutz@umich.edu
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4937-4947 - MSC (2010): Primary 52C35; Secondary 05B35, 16S37
- DOI: https://doi.org/10.1090/proc/14591
- MathSciNet review: 4011525