17 may 2017 -- 13:00
Aula D'Antoni, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
In 1989 Manin and Schechtman considered a family of arrangements of hyperplanes generalizing classical braid arrangements which they called the Discriminantal arrangements. Such an arrangement consists of parallel translates of collection of n hyperplanes in general position in Ck which fail to form a generic arrangement in Ck. In 1994 Falk showed that the combinatorial type of Discriminantal arrangement depends on the collection of n hyperplanes in general position in Ck. In 1997 Bayer and Brandt divided generic arrangements in Ck in 'very generic' and 'non very generic' depending of the intersection lattice of associated Discriminatal arrangement. In 1999 Athanasiadis provided a full description of intersection lattice for Discriminantal arrangement in the very generic case. More recently, in 2016, Libgober and Settepanella gave a description of rank 2 intersection lattice of Discriminantal arrangement in non very generic case, providing a sufficient geometric condition for a generic arrangement in Ck to be non very generic. In this talk we will recall their result and we will show that non very generic arrangements in C3 satisfying their condition correspond to points in a degree 2 hypersurface in the complex Grassmannian Gr(3,n). This is a joint work with S. Sawada and S. Yamagata.