阿部 拓郎 (京都大学）「Divisionally free arrangements of hyperplanes」
The freeness of hyperplane arrangements has been one of the most important topics in this research area. In particular, Terao's conjecture asserting whether the freeness depends only on the combinatorics of arrangements is the important long standing problem. In this talk, we introduce the new class of free arrangements called divisionally free, and show that their freeness depends only on combinatorics. This class contains the classical large class of inductively free arrangements in which also Terao's conjecture is true. We also give several applications on the freeness of arrangements related to the root system.