On projective wonderful models for toric arrangements and their cohomology

Concini, Corrado De; Gaiffi, Giovanni; Papini, Oscar

doi:10.1007/s40879-020-00414-z

Cited by 7 publications

(6 citation statements)

References 28 publications

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“…The definitions of building sets and nested sets are recalled in this section. Example 2.1 provides a non trivial instance in dimension 3 of this construction, computed with the help of a SageMath program (see [13]).…”

Section: Structure Of This Papermentioning

confidence: 99%

“…In this section we recall the construction of a wonderful model starting from a toric arrangement A, mainly following [10] (see also [13]).…”

Section: Brief Description Of Compact Modelsmentioning

confidence: 99%

“…The building set G described in Example 2.1 is a well-connected building set. Some general properties of well-connected building sets are studied and presented in [13,Section 6].…”

Section: Presentation Of the Cohomology Ringmentioning

confidence: 99%

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A basis for the cohomology of compact models of toric arrangements

Gaiffi¹,

Papini²,

Siconolfi³

2022

Preprint

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In this paper we find monomial bases for the integer cohomology rings of compact wonderful models of toric arrangements. In the description of the monomials various combinatorial objects come into play: building sets, nested sets, and the fan of a suitable toric variety. We provide some examples computed via a SageMath program and then we focus on the case of the toric arrangements associated with root systems of type A.Here the combinatorial description of our basis offers a geometrical point of view on the relation between some Eulerian statistics on the symmetric group.

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Section: Structure Of This Papermentioning

confidence: 99%

“…In this section we recall the construction of a wonderful model starting from a toric arrangement A, mainly following [10] (see also [13]).…”

Section: Brief Description Of Compact Modelsmentioning

confidence: 99%

See 1 more Smart Citation

A basis for the cohomology of compact models of toric arrangements

Gaiffi¹,

Papini²,

Siconolfi³

2022

Preprint

Self Cite

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“…Background. We recall basic terminology concerning toric arrangements, studied in, e.g., [14], [12], [10], [9], [11], [4], [2].…”

Section: Stabilizer Stratification and Subdivisionsmentioning

confidence: 99%

Equivariant Burnside groups and toric varieties

Kresch¹,

Tschinkel²

2021

Preprint

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“…The notion of wonderful compactification firstly appeared in the paper [11] of De Concini-Procesi in the context of an equivariant compactification of the symmetric spaces G/H, see also [23] and [26] for a comprehensive overview of the subject. This idea has been further developed and applied in many directions, such as Fulton-MacPherson compactification in [13], De Concini-Procesi wonderful models [11], [12], the wonderful compactification of Li [22] and more recently the projective wonderful models of toric arrangements by De Concini-Gaiffi and others [7], [8], [9]. Furthermore, this paper finds the advantage of wonderful compactification for the description of the equivariant topology of the Grassmannians G n,2 for the canonical T n -action.…”

Section: Introductionmentioning

confidence: 99%

The orbit spaces $G_{n,2}/T^n$ and the Chow quotients $G_{n,2}\!/\!/(\mathbb{C} ^{\ast})^{n}$ of the Grassmann manifolds $G_{n,2}$

Buchstaber,

Terzić

2021

Preprint

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The focus of our paper is on the complex Grassmann manifolds G n,2 which appear as one of the fundamental objects in developing the interaction between algebraic geometry and algebraic topology. In his wellknown paper Kapranov has proved that the Deligne-Mumford compactification M(0, n) of n-pointed curves of genus zero can be realized as the Chow quotient G n,2 //(C * ) n . In our recent papers, the constructive description of the orbit space G n,2 /T n has been obtained. In getting this result our notions of the CW-complex of the admissible polytopes and the universal space of parameters F n for T n -action on G n,2 were of essential use. Using technique of the wonderful compactification, in this paper it is given an explicit construction of the space F n . Together with Keel's description of M(0, n), this construction enabled us to obtain an explicit diffeomorphism between F n and M(0, n). Thus, we showed that the space G n,2 //(C * ) n can be realized as our universal space of parameters F n . In this way, we give description of the structure in G n,2 //(C * ) n , that is M(0, n) in terms of the CW-complex of the admissible polytopes for G n,2 and their spaces of parameters. 1

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On projective wonderful models for toric arrangements and their cohomology

Abstract: 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 (

Cited by 7 publications

References 28 publications

A basis for the cohomology of compact models of toric arrangements

A basis for the cohomology of compact models of toric arrangements

Equivariant Burnside groups and toric varieties

The orbit spaces $G_{n,2}/T^n$ and the Chow quotients $G_{n,2}\!/\!/(\mathbb{C} ^{\ast})^{n}$ of the Grassmann manifolds $G_{n,2}$

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