10 citations · 16 across the 9 of their papers we have counts for
10 papers
Milnor fibrations and oriented matroids
Paul Mücksch, Masahiko Yoshinaga
We introduce a combinatorial model for the Milnor fibration of a complexified real arrangement using oriented matroids. It is a poset quasi-fibration, whose domain is a subdivision…
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 …
Projective dimension of weakly chordal graphic arrangements
Takuro Abe, Lukas Kühne, Paul Mücksch +1
A graphic arrangement is a subarrangement of the braid arrangement whose set of hyperplanes is determined by an undirected graph. A classical result due to Stanley, Edelman and Rei…
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…
Modular flats of oriented matroids and poset quasi-fibrations
Paul Mücksch
We study the combinatorics of modular flats of oriented matroids and the topological consequences for their Salvetti complexes. We show that the natural map to the localized Salvet…
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…
On Yuzvinsky's lattice sheaf cohomology for hyperplane arrangements
Paul Mücksch
We establish the relationship between the cohomology of a certain sheaf on the intersection lattice of a hyperplane arrangement introduced by Yuzvinsky and the cohomology of the co…
Accurate Arrangements
Paul Mücksch, Gerhard Roehrle
Let be a Coxeter arrangement of rank . In 1987 Orlik, Solomon and Terao conjectured that for every , the first exponents of -…
Supersolvable simplicial arrangements
Michael Cuntz, Paul Mücksch
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank th…