Accurate arrangements

Let A be a Coxeter arrangement of rank ℓ. In 1987 Orlik, Solomon and Terao conjectured that for every 1≤d≤ℓ, the first d exponents – when listed in increasing order are realized as free restriction to some intersection reflecting hyperplanes dimension d. This conjecture does follow from rather extensive case-by-case studies by Orlik 1992 1993, where they show all restrictions arrangements free. We call general with this natural property involving their accurate. paper we initialize systematic study. Our principal result shows MAT-free arrangements, notion recently introduced Cuntz Mücksch, theorem turn directly implies special ideal subarrangements Weyl arrangements. particular, gives new, simpler uniform proof aforementioned which is any considerations. Another application slightly more formulation our main extended Catalan Shi ideal-Shi share well. also study satisfy weaker condition, called almost accurate simply disregard ordering involved. implied many well established concepts freeness such supersolvability divisional freeness.