A generalization of fiber-type arrangements and a new deformation method

We introduce the hypersolvable class of arrangements which contains the fiber-type ones of [14], then extend and refine various results concerning the topology of the complement, in its interplay with the combinatorics, to this new class. We prove that the K(pi, 1) property is combinatorial in the hypersolvable class, along with some other properties conjectured to be related to asphericity in [15]. We describe the structure of the fundamental groups of hypersolvable complements and prove that their associated graded Lie algebras are always determined by a minimal combinatorial information. We develop a deformation method for producing fibrations of arrangement spaces and emphasize throughout the role played by the quadratic Orlik-Solomon algebra, a variation on a classical combinatorial theme of [27]. We prove that for hypersolvable arrangements the quadratic Orlik-Solomon algebra is always Koszul and also use it to obtain a generalization of the lower central series formula of [14]. (C) 1998 Elsevier Science Ltd. All rights reserved.