MS Seminar (Mathematics - String Theory)

Speaker: Takuro Abe (Kyushu U)
Title: Divisionally free arrangements of hyperplanes
Date: Thu, Jun 16, 2016, 15:30 - 17:00
Place: Seminar Room A
Abstract: Free arrangements of hyperplanes were introduced by K. Saito in 1970's. There are a lot of ways to understand free arrangements, but one of them is a generalization of Weyl arrangements and groups in terms of their exponents, i.e., by using logarithmic vector fields of free arrangements, we can define their exponents, and they describe the topological Poincare polynomial of the complement of hyperplanes as for Weyl group case.

However, how to determine freeness of an arrangements has been a difficult problem. The most useful way is a constructive approach by Terao, the addition-deletion theorem. In this talk, we give an improvement of the addition-deletion theorem, so called the division theorem. By using this, we can construct several free arrangements efficiently, and also we can determine those freeness depends only on the combinatorial structure of arrangements. To state it systematically, we introduce the category of divisionally free arrangements.