Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n)

We show that points in specific degree-2 hypersurfaces in the Grassmannian $Gr(3,n)$ correspond to generic arrangements of n hyperplanes in ${\mathbb{C}}^3$ with associated discriminantal arrangement having intersections of multiplicity three in codimension two.     

Divide and conquer: the engineering of delegation

Computational Management Science - Members of an organization have conflicting preferences. Principal-agent theory analyzes how and under which conditions this conflict can be resolved by means of...     

Cohomology of Pure Braid Groups of exceptional cases

Consider the ring R:=Q[τ,τ−1] of Laurent polynomials in the variable τ. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over R, where the action of every standard generator is the multiplication by τ. In this paper we consider the cohomology of these groups with coefficients in the module R (it is well known that such cohomology is strictly related to the untwisted integral cohomology of the Milnor fibration naturally associated to the reflection arrangement). We compute this cohomology for the cases I₂(m), H₃, H₄, F₄ and An with 1?n?7.