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On the non-very generic intersections in discriminantal arrangements.
- Source :
-
Comptes Rendus. Mathématique . 2022, Vol. 360, p1027-1038. 12p. - Publication Year :
- 2022
-
Abstract
- In 1985 Crapo introduced in [3] a new mathematical object that he called geometry of circuits. Four years later, in 1989, Manin and Schechtman defined in [13] the same object and called it discriminantal arrangement, the name by which it is known now a days. Those discriminantal arrangements B(n,k,A 0 ) are builded from an arrangement A 0 of n hyperplanes in general position in a k-dimensional space and their combinatorics depends on the arrangement A 0 . On this basis, in 1997 Bayer and Brandt (see [2]) distinguished two different type of arrangements A 0 calling very generic the ones for which the intersection lattice of B(n,k,A 0 ) has maximum cardinality and non-very generic the others. Results on the combinatorics of B(n,k,A 0 ) in the very generic case already appear in Crapo [3] and in 1997 in Athanasiadis [1] while the first known result on non-very generic case is due to Libgober and the first author in 2018. In their paper [12] they provided a necessary and sufficient condition on A 0 for which the cardinality of rank 2 intersections in B(n,k,A 0 ) is not maximal anymore. In this paper we further develop their result providing a sufficient condition on A 0 for which the cardinality of rank r, r ≥ 2, intersections in B(n,k,A 0 ) decreases. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMBINATORICS
*GEOMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 1631073X
- Volume :
- 360
- Database :
- Academic Search Index
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- 173500307
- Full Text :
- https://doi.org/10.5802/crmath.360