2022/02/10 by Takuya Saito, Saito, Takuya, Simona Settepanella +1 · 1 citation
Mathematics · #05B35 #52C35 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2202.04794
openalex publication_date 2022/02/10 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
The discriminantal arrangement B(n,k,A) has been introduced by Manin and Schectman in 1989 and it consists of all non-generic translates of a generic arrangement A of n hyperplanes in a k-dimensional space. It is known that its combinatorics depends on the original arrangement A which, following Bayer and Brandt [3], is called very generic if the intersection lattice of the induced discriminantal arrangement has maximum cardinality, non-very generic otherwise. While a complete description of the combinatorics of B(n,k,A) when A is very generic is known (see [2]), very few is known in the non-very generic case. Even to provide examples of non very generic arrangements proved to be a non-trivial task (see [17]). In this paper, we characterize, classify and provide examples of non-very generic arrangements in low dimension.