Results 11 to 20 of about 344 (154)
Combinatorics of toric arrangements [PDF]
Rendiconti Lincei, Matematica e Applicazioni, 2019 In this paper we build an Orlik–Solomon model for the canonical gradation of the cohomology algebra with integer coefficients of the complement of a toric arrangement. We give some results on the uniqueness of the representation of arithmetic matroids, in order to discuss how the Orlik–Solomon model depends on the poset of layers.
Pagaria R.
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A Tutte polynomial for toric arrangements [PDF]
Transactions of the American Mathematical Society, 2012 Final version, to appear on Transactions AMS.
Luca Moci, Moci L
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The integer cohomology of toric Weyl arrangements [PDF]
, 2010 A referee found an error in the proof of the Theorem 2 that we could not fix. More precisely, the proof of Lemma 2.1 is incorrect. Hence the fact that integer cohomology of complement of toric Weyl arrangements is torsion free is still a conjecture. ----- A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being ...
Simona Settepanella
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Cohomology rings of compactifications of toric arrangements [PDF]
Algebraic & Geometric Topology, 2019 A new section (Section 9) has been added, to include the presentation of the cohomology rings of all the strata in the ...
De Concini +2 more
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A differential algebra and the homotopy type of the complement of a toric arrangement [PDF]
Rendiconti Lincei, Matematica e Applicazioni, 2021 We show that the rational homotopy type of the complement of a toric arrangement is completely determined by two sets of discrete data. This is obtained by introducing a differential graded algebra over Q whose minimal model is equivalent to the Sullivan minimal model of \mathcal A
De Concini C., Gaiffi G.
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Zonotopes, toric arrangements, and generalized Tutte polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 We introduce a multiplicity Tutte polynomial $M(x,y)$, which generalizes the ordinary one and has applications to zonotopes and toric arrangements. We prove that $M(x,y)$ satisfies a deletion-restriction recurrence and has positive coefficients.
Luca Moci, Moci, Luca, Moci L
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Orlik-Solomon type presentations for the cohomology algebra of toric arrangements [PDF]
Transactions of the American Mathematical Society, 2019 We give an explicit presentation for the integral cohomology ring of the complement of any arrangement of level sets of characters in a complex torus (alias "toric arrangement"). Our description parallels the one given by Orlik and Solomon for arrangements of hyperplanes, and builds on De Concini and Procesi's work on the rational cohomology of ...
Callegaro, Filippo +5 more
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Hyperbolic structures on a toric arrangement complement
, 2015 This thesis studies the geometric structures on toric arrangement complements. Inspired by the special hypergeometric functions associated with a root system, we consider a family of connections on a total space which is the product of the complement of a toric arrangement (=finite union of hypertori) and $\mathbb{C}^{\times}$.
Shen, Dali +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 ...
Norledge, William
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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 ...
Luca Moci, MOCI, LUCA, Moci L
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