離散幾何構造セミナー：Discriminantal Arrangement, 3×3 Minors of Plücker Matrix and Hypersurfaces in Grassmannian Gr(3,n)

開催日時

2018年1月25日 11時00分 ～ 2018年1月25日 11時20分

場所

3-413

講演者

山形 颯

DGS Seminar 012

For a generic arrangement of n hyperplanes A = { H^0_1, H^0_2, …, H^0_n } in C^k, k
The closed subset of S formed by translates of hyperplanes in A that fail to form a generic arrangement defines an arrangement of hyperplanes. This arrangement B(n,k) is defined by Manin and Schechtman in 1989 and called the discriminantal arrangement.

In 1999 Falk showed that the combinatorial type of B(n,k) depends on original arrangement by providing an example. In 1997 Bayer and Brandt called an arrangement A very generic if for any rank the cardinality of intersection lattice of B(n, k) is the maximum possible number and non very generic otherwise. They conjectured a description of combinatorics of discriminantal arrangement associated to very generic arrangement. In 1999 Athanasiadis proved their conjecture and so a full description of discriminantal arrangement for very generic arrangement was completed. However for non very generic arrangements description of combinatorics of discriminantal arrangement is only known for rank 2 intersections (by a work of Libgober and Settepanella).