Results 1 to 10 of about 207 (98)
Cohomology of complements of toric arrangements associated with root systems [PDF]
Research in Mathematical Sciences, 2022 We develop an algorithm for computing the cohomology of complements of toric arrangements. In the case a finite group ΓΓ is acting on the arrangement, the algorithm determines the cohomology groups as representations of ΓΓ.
Olof Bergvall
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The integer cohomology algebra of toric arrangements [PDF]
Advances in Mathematics, 2017 We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data.
Filippo Callegaro, Emanuele Delucchi
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Wonderful Models for Toric Arrangements [PDF]
International Mathematics Research Notices, 2012 We build a wonderful model for toric arrangements. We develop the "toric analog" of the combinatorics of nested sets, which allows us to define a family of smooth open sets covering the model. In this way, we prove that the model is smooth, and we give a
Luca Moci
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On the geometry of toric arrangements [PDF]
Transformation Groups, 2005 Motivated by the counting formulas of integral polytopes, as in Brion and Vergne [5], [4], and Szenes and Vergne [27], we start to form the foundations of a theory for toric arrangements, which may be considered as the periodic version of the theory of ...
Procesi C
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Projective wonderful models for toric arrangements [PDF]
Advances in Mathematics, 2018 In this paper we illustrate an algorithmic procedure which allows to build projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T.
Corrado De Concini, Giovanni Gaiffi
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Two examples of toric arrangements [PDF]
Journal of Combinatorial Theory - Series A, 2019 We show that the integral cohomology algebra of the complement of a toric arrangement is not determined by the poset of layers. Moreover, the rational cohomology algebra is not determine by the arithmetic matroid (however it is determine by the poset of ...
Roberto Pagaria
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On projective wonderful models for toric arrangements and their cohomology [PDF]
European Journal of Mathematics, 2020 This paper is divided into two parts. The first part is a brief survey, accompanied by concrete examples, on the main results of the papers (De Concini and Gaiffi in Adv Math 327:390–09, 2018; Algebr Geom Topol 19(1):503–532, 2019): the construction
Corrado De Concini +2 more
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Arithmetic matroids, the Tutte polynomial and toric arrangements [PDF]
Advances in Mathematics, 2013 We introduce the notion of an arithmetic matroid whose main example is 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.
Luca Moci
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Cohomology rings of compactifications of toric arrangements [PDF]
Algebraic and Geometric Topology, 2019 Some projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T were constructed in [3].
Corrado De Concini +2 more
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Face counting formula for toric arrangements defined by root systems [PDF]
AKCE International Journal of Graphs and Combinatorics, 2019 A toric arrangement is a finite collection of codimension-1 subtori in a torus. The intersections of these subtori stratify the ambient torus into faces of various dimensions.
Priyavrat Deshpande
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