Arrangements of Hyperplanes

affine algebra arrangement assertion associated assume basic basis for D(A braid called central arrangement choose complement complex compute consider consisting construct contains Corollary corresponding Define Definition deletion denote dependent derivations Derk(S determined direct elements equal equivalent exact Example exists face factorization Figure finite follows from Lemma formula free arrangement function given gives graded graph hence homogeneous homotopy hyperplanes ideal implies inclusion independent induction integers invariants irreducible isomorphism K-module lattice linear linearly lines Math matrix maximal module natural Note obtained Orbits pair partition plane Poincaré polynomial points polynomial poset positive projection Proof properties Proposition prove rank Recall reflection group restriction result satisfies sequence space subset supersolvable Suppose surjective Table Theorem theory triple unique vertices write