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Let $\mathcal A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $\mathcal A"$ of $\mathcal A$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement. In 2024, the first two aut
Externí odkaz:
http://arxiv.org/abs/2210.00436
Autor:
Hoge, Torsten, Roehrle, Gerhard
Let $\mathcal A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $\mathcal A''$ of $\mathcal A$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement $(\mathcal A'',\kappa)$. T
Externí odkaz:
http://arxiv.org/abs/2204.09540
Autor:
Hoge, Torsten, Roehrle, Gerhard
We exhibit a particular free subarrangement of a certain restriction of the Weyl arrangement of type $E_7$ and use it to give an affirmative answer to a recent conjecture by T.~Abe on the nature of additionally free and stair-free arrangements.
Externí odkaz:
http://arxiv.org/abs/1903.01438
Autor:
Hoge, Torsten, Roehrle, Gerhard
Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger freeness property of indu
Externí odkaz:
http://arxiv.org/abs/1705.02767
In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to multi-arrangements stemming from well
Externí odkaz:
http://arxiv.org/abs/1703.08980
Akademický článek
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Autor:
Hoge, Torsten, Roehrle, Gerhard
The aim of this note is a classification of all nice and all inductively factored reflection arrangements. It turns out that apart from the supersolvable instances only the monomial groups $G(r,r,3)$ for $r \ge 3$ give rise to nice reflection arrange
Externí odkaz:
http://arxiv.org/abs/1505.04603
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 application, we prove that recursively free multiarrangements are compatibl
Externí odkaz:
http://arxiv.org/abs/1501.06312
Autor:
Hoge, Torsten, Roehrle, Gerhard
In 1989, Ziegler introduced the concept of a multi-arrangement. One natural example is the reflection arrangement of a unitary reflection group with multiplicity given by the number of reflections associated with each hyperplane. For all but three ir
Externí odkaz:
http://arxiv.org/abs/1403.4725
Autor:
Hoge, Torsten, Roehrle, Gerhard
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 celebrated addition-deletion theorem for free arrangements for the class
Externí odkaz:
http://arxiv.org/abs/1402.3227