Simplicial arrangements on convex cones

Some Results on Boundedness in Locally Convex Cones

Cones of Hilbert Functions

We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the cones generated by the Hilbert functions of all modules, all modules with bounded a-invariant, and all modules with bounded Castelnuovo–Mumford regularity. The f...

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

On a Parametrization of Positive Semidefinite Matrices with Zeros

We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a polynomial map associated with a simplicial complex supported on cliques of the graph. The images of the maps are convex cones, and the maps can only be surjecti...

Bishop-Phelps type Theorem for Normed Cones

In this paper the notion of  support points of convex sets  in  normed cones is introduced and it is shown that in a  continuous normed cone, under the appropriate conditions, the set of support points of a  bounded Scott-closed convex set is nonempty. We also present a Bishop-Phelps type Theorem for normed cones.