Document - A basis for the cohomology of compact models of toric arrangements

2024

Journal article Open Access

A basis for the cohomology of compact models of toric arrangements

Gaiffi G, Papini O., Siconolfi V.

Eulerian numbers Configuration spaces Compact models Mathematics - Algebraic Topology FOS: Mathematics Toric arrangements Algebraic Topology (math.AT) Mathematics - Combinatorics Combinatorics (math.CO)

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.

Source: PURE AND APPLIED MATHEMATICS QUARTERLY, vol. 20 (issue 1), pp. 427-470

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@article{oai:iris.cnr.it:20.500.14243/501381,
	title = {A basis for the cohomology of compact models of toric arrangements},
	author = {Gaiffi G and Papini O. and Siconolfi V.},
	doi = {10.4310/pamq.2024.v20.n1.a9 and 10.48550/arxiv.2205.00443},
	year = {2024}
}