Geodesic
Discriminantal arrangements, fiber polytopes and formality
Journal of Algebraic Combinatorics, Tome 6 (1997) no. 3, pp. 229-246.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Manin and Schechtman defined the discriminantal arrangement of a generic hyperplane arrangement as a generalization of the braid arrangement. This paper shows their construction is dual to the fiber zonotope construction of Billera and Sturmfels, and thus makes sense even when the base arrangement is not generic. The hyperplanes, face lattices and intersection lattices of discriminantal arrangements are studied. The discriminantal arrangement over a generic arrangement is shown to be formal (and in some cases 3-formal), though it is in general not free. An example of a free discriminantal arrangement over a generic arrangement is given.
Keywords: discriminantal arrangement, hyperplane arrangement, polytope, free 
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     title = {Discriminantal arrangements, fiber polytopes and formality},
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Bayer, Margaret M.; Brandt, Keith A. Discriminantal arrangements, fiber polytopes and formality. Journal of Algebraic Combinatorics, Tome 6 (1997) no. 3, pp. 229-246. http://geodesic.mathdoc.fr/item/JAC_1997__6_3_a6/