Results 21 to 30 of about 94 (68)
Free arrangements of hyperplanes and supersolvable lattices
Advances in Mathematics, 1984 The authors investigate the relation between two different concepts that come up with an arrangement A of hyperplanes through the origin in \({\mathbb{C}}^{\ell +1}\). On one hand, A is said to be free if the corresponding module of logarithmic vector fields is a free module.
Jambu, Michel, Terao, Hiroaki
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On supersolvable reflection arrangements
, 2012 13 pages, updated references, to appear in Proc. Amer. Math. Soc. v3.
Hoge, Torsten, Roehrle, Gerhard
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Vertex-weighted Digraphs and Freeness of Arrangements Between Shi and Ish
, 2021 We introduce and study a digraph analogue of Stanley's $\psi$-graphical arrangements from the perspectives of combinatorics and freeness. Our arrangements form a common generalization of various classes of arrangements in literature including the Catalan
Tsujie, Shuhei +2 more
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Koszulness and supersolvability for Dirichlet arrangements
Proceedings of the American Mathematical Society, 2019 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.
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The e-multiplicity and addition-deletion theorems for multiarrangements [PDF]
, 2006 The addition-deletion theorems for hyperplane arrangements, which were originally shown in [T1], provide useful ways to construct examples of free arrangements. In this article, we prove addition-deletion theorems for multiarrangements.
Abe, Takuro +2 more
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Holonomy Lie algebra of a geometric lattice
, 2023 Motivated by Kohno's result on the holonomy Lie algebra of a hyperplane arrangement, we define the holonomy Lie algebra of a finite geometric lattice in a combinatorial way.
Liu, Ye, Guo, Weili
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Cones of Hyperplane Arrangements [PDF]
, 2021 University of Minnesota Ph.D. dissertation. July 2021. Major: Mathematics. Advisor: Victor Reiner. 1 computer file (PDF); vii, 113 pages.Hyperplane arrangements dissect $\R^n$ into connected components called chambers, and a well-known theorem of ...
Dorpalen-Barry, Galen
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The $\textbf{nbc}$ minimal complex of supersolvable arrangements
, 2015 In this paper we give a very natural description of the bijections between the minimal CW-complex homotopy equivalent to the complement of a supersolvable arrangement $\mathcal{A}$, the $\textbf{nbc}$ basis of the Orlik-Solomon algebra associated to $\mathcal{A}$ and the set of chambers of $\mathcal{A}$.
Settepanella, Simona, Torielli, Michele
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A Geometric Condition for a Hyperplane Arrangement to be Free
, 1998 LetG(r, 1, l) be the complex arrangement {xi, xj−ξhxk}, whereξis a primitiverth root of unity. The matroids of these arrangements are the Dowling matroidsQl(Zr), whereZris the group ofrth roots of unity.
Kung, Joseph P.S.
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Monodromy of supersolvable toric arrangements
We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and bundles involving classical configuration spaces.
Bibby, Christin +2 more
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