Details
| Original language | English |
|---|---|
| Pages (from-to) | 439-458 |
| Number of pages | 20 |
| Journal | Beitrage zur Algebra und Geometrie |
| Volume | 56 |
| Issue number | 2 |
| Publication status | Published - 28 Oct 2015 |
Abstract
We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present some series of arrangements related to the known arrangements in characteristic zero. We further enumerate simplicial arrangements with given symmetry groups. Finally, we determine all finite complex reflection groups affording combinatorially simplicial arrangements. It turns out that combinatorial simpliciality coincides with inductive freeness for finite complex reflection groups except for the Shephard–Todd group (Formula presented.).
Keywords
- Arrangement of hyperplanes, Projective plane, Simplicial
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Geometry and Topology
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In: Beitrage zur Algebra und Geometrie, Vol. 56, No. 2, 28.10.2015, p. 439-458.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Combinatorial simpliciality of arrangements of hyperplanes
AU - Cuntz, M.
AU - Geis, D.
PY - 2015/10/28
Y1 - 2015/10/28
N2 - We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present some series of arrangements related to the known arrangements in characteristic zero. We further enumerate simplicial arrangements with given symmetry groups. Finally, we determine all finite complex reflection groups affording combinatorially simplicial arrangements. It turns out that combinatorial simpliciality coincides with inductive freeness for finite complex reflection groups except for the Shephard–Todd group (Formula presented.).
AB - We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present some series of arrangements related to the known arrangements in characteristic zero. We further enumerate simplicial arrangements with given symmetry groups. Finally, we determine all finite complex reflection groups affording combinatorially simplicial arrangements. It turns out that combinatorial simpliciality coincides with inductive freeness for finite complex reflection groups except for the Shephard–Todd group (Formula presented.).
KW - Arrangement of hyperplanes
KW - Projective plane
KW - Simplicial
UR - http://www.scopus.com/inward/record.url?scp=84940506389&partnerID=8YFLogxK
U2 - 10.1007/s13366-014-0190-x
DO - 10.1007/s13366-014-0190-x
M3 - Article
AN - SCOPUS:84940506389
VL - 56
SP - 439
EP - 458
JO - Beitrage zur Algebra und Geometrie
JF - Beitrage zur Algebra und Geometrie
SN - 0138-4821
IS - 2
ER -