9 citations · 39 across the 30 of their papers we have counts for
14 papers · 1 filter
On connected subgraph arrangements
Lorenzo Giordani, Tilman Möller, Paul Mücksch +1
Recently, Cuntz and Kühne introduced a particular class of hyperplane arrangements stemming from a given graph , so called connected subgraph arrangements . In this note we…
Free multiderivations of connected subgraph arrangements
Paul Mücksch, Gerhard Roehrle, Sven Wiesner
Cuntz and Kühne introduced the class of connected subgraph arrangements , depending on a graph , and classified all graphs such that the corresponding arrangement …
Flag-accurate arrangements
Paul Mücksch, Gerhard Roehrle, Tan Nhat Tran
In [MR21], the first two authors introduced the notion of an accurate arrangement, a particular notion of freeness. In this paper, we consider a special subclass, where the propert…
Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements
Torsten Hoge, Gerhard Roehrle, Sven Wiesner
Let be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction of to any hyperplane endowed with the natural multiplicit…
Inductive Freeness of Ziegler's Canonical Multiderivations
Torsten Hoge, Gerhard Roehrle
Let be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction of to any hyperplane endowed with the natural multiplici…
On Formality and Combinatorial Formality for hyperplane arrangements
Tilman Möller, Paul Mücksch, Gerhard Roehrle
A hyperplane arrangement is called formal provided all linear dependencies among the defining forms of the hyperplanes are generated by ones corresponding to intersections of codim…
Arrangements of ideal type are inductively free
Michael Cuntz, Gerhard Roehrle, Anne Schauenburg
Extending earlier work by Sommers and Tymoczko, in 2016 Abe, Barakat, Cuntz, Hoge, and Terao established that each arrangement of ideal type stemming from…
Inductive Freeness of Ziegler's Canonical Multiderivations for Reflection Arrangements
Torsten Hoge, Gerhard Roehrle
Let be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction of to any hyperplane endowed with the natural multiplicity is then a free multiarra…
Nice Restrictions of Reflection Arrangements
Tilman Moeller, Gerhard Roehrle
In a recent paper, Hoge and the second author classified all nice and all inductively factored reflection arrangements. In this note we extend this classification by determining al…
Arrangements of ideal type
Gerhard Roehrle
In 2006 Sommers and Tymoczko defined so called arrangements of ideal type A_I stemming from ideals I in the set of positive roots of a reduced root system. They showed in a case by…
Inductively free Multiderivations of Braid arrangements
Henning Conrad, Gerhard Roehrle
The reflection arrangement of a Coxeter group is a well known instance of a free hyperplane arrangement. In 2002, Terao showed that equipped with a constant multiplicity each such…
Inductive and Recursive Freeness of Localizations of Multiarrangements
Torsten Hoge, Gerhard Roehrle, Anne Schauenburg
The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an appli…
Addition-Deletion Theorems for Factorizations of Orlik-Solomon Algebras and nice Arrangements
Torsten Hoge, Gerhard Roehrle
We study the notion of a nice partition or factorization of a hyperplane arrangement due to Terao from the early 1990s. The principal aim of this note is an analogue of Terao's cel…
Supersolvable restrictions of reflection arrangements
N. Amend, T. Hoge, G. Roehrle
Let A = (A,V) be a complex hyperplane arrangement and let L(A) denote its intersection lattice. The arrangement A is called supersolvable, provided its lattice L(A) is supersolvabl…