Supersolvable arrangement

In mathematics, a supersolvable arrangement is a hyperplane arrangement that has a maximal flag consisting of modular elements. Equivalently, the intersection semilattice of the arrangement is a supersolvable lattice, in the sense of Richard P. Stanley.^[1] As shown by Hiroaki Terao, a complex hyperplane arrangement is supersolvable if and only if its complement is fiber-type.^[2]

Examples include arrangements associated with Coxeter groups of type A and B.

The Orlik–Solomon algebra of every supersolvable arrangement is a Koszul algebra; whether the converse is true is an open problem.^[3]