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Wonderful Models for Generalized Dowling Arrangements

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Abstract

For any triple given by a positive integer n, a finite group G, and a faithful representation V of G, one can describe a subspace arrangement whose intersection lattice is a generalized Dowling lattice in the sense of Hanlon (Trans. Amer. Math. Soc. 325(1), 1–37, 1991). In this paper we construct the minimal De Concini-Procesi wonderful model associated to this subspace arrangement and give a description of its boundary. Our aim is to point out the nice poset provided by the intersections of the irreducible components in the boundary, which provides a geometric realization of the nested set poset of this generalized Dowling lattice. It can be represented by a family of forests with leaves and labelings that depend on the triple (n,G,V ). We will study it from the enumerative point of view in the case when G is abelian.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Giovanni Gaiffi

  2. Dipartimento di Matematica, Università di Roma Tor Vergata, Rome, Italy

    Viola Siconolfi

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  1. Giovanni Gaiffi
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  2. Viola Siconolfi
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Correspondence to Viola Siconolfi.

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Gaiffi, G., Siconolfi, V. Wonderful Models for Generalized Dowling Arrangements. Order 37, 605–620 (2020). https://doi.org/10.1007/s11083-019-09521-3

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  • DOI: https://doi.org/10.1007/s11083-019-09521-3

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