Results 61 to 70 of about 207 (98)
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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Braid arrangement bimonoids and the toric variety of the permutohedron
, 2022 We show that the toric variety of the permutohedron (=permutohedral space) has the structure of a cocommutative bimonoid in species, with multiplication/comultiplication given by embedding/projecting-onto boundary divisors. In terms of Losev-Manin's description of permutohedral space as a moduli space, multiplication is concatenation of strings of ...
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Combinatorics and topology of toric arrangements defined by root systems
Rendiconti Lincei, Matematica e Applicazioni, 2008 Given the toric (or toral) arrangement defined by a root system \Phi , we classify and count its components of each dimension. We show how to reduce to the case of 0-dimensional components, and in this case we give an explicit formula involving the ...
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Geometry and combinatorics of toric arrangements
, 2010 A toric arrangement is a finite set of hypersurfaces in a complex torus, each hypersurface being the kernel of a character. In the first chapter we focus on the case of toric arrangements defined by root systems: by describing the action of the Weyl ...
Moci, Luca
core
Erratum to "The integer cohomology algebra of toric arrangements"
, 2021 We correct two errors in the paper ``The integer cohomology algebra of toric arrangements'', Adv. Math., Vol. 313, pp. 746-802, 2017. The main error concerns Theorem 4.2.17. In that theorem's proof, Diagram (8) does not commute in general but only under
Emanuele Delucchi, Filippo Callegaro
core
Computing the poset of layers of a toric arrangement
, 2017 A toric arrangement is an arrangement of subtori of codimension one in a real or complex torus. The poset of layers is the set of connected components of non-empty intersections of these subtori, partially ordered by reverse inclusion. In this note we present an algorithm that computes this poset in the central case.
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The Goresky-MacPherson formula for toric arrangements
, 2018 A subspace arrangement is a finite collection of affine subspaces in $\mathbb{R}^n$. One of the main problems associated to arrangements asks up to what extent the topological invariants of the union of these spaces, and of their complement are determined by the combinatorics of their intersection.
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Arithmetic matroids, Tutte polynomial, and toric arrangements
, 2011 We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality to this setting.
D'Adderio, Michele, Moci, Luca
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A Tutte polynomial for toric arrangements
, 2010 We introduce a multiplicity Tutte polynomial M(x, y), with applications to zonotopes and toric arrangements. We prove that M(x, y) satisfies a deletion-restriction recursion and has positive coefficients.
Luca Moci
core
On the cohomology of arrangements of subtori
, 2020 Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology.
Moci, Luca, Pagaria, Roberto
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