Factored arrangements of hyperplanes
The paper discusses factored arrangements \(\mathcal A\) of hyperplanes in finite-dimensional complex spaces. Roughly speaking, an arrangement \(\mathcal A\) is factored if it allows a suitable ``nice'' partition (factorization) into smaller sets of hyperplanes. The existence of a factorization translates into a factorization of the associated Orlik-Solomon algebra (cohomology algebra of the complement) and the corresponding Poincaré polynomial. An arrangement \(\mathcal A\) is inductively factored it it has a stronger kind of factorization (called inductive factorization). The authors survey and explain the results they have obtained in their paper in Eur. J. Comb. 16, No. 3, 267-292 (1995; see the review above). These include that inductively factored arrangements are free, and in the real case that the rank generating function for a certain poset which is naturally associated with the underlying chamber complex factors nicely.
scientific article; zbMATH DE number 729231
scientific article