We study the realization spaces of matroids and hyperplane arrangements. First, we define
the notion of naive dimension for the realization space of matroids and compare it with the …

In this paper we introduce a natural model for the realization space of a polytope up to
projective equivalence which we call the slack realization space of the polytope. The model …

We introduce a new method for finding a non-realizability certificate of a simplicial sphere Σ:
we exhibit a monomial combination of classical 3-term Plücker relations that yields a sum of …

The slack ideal of a polytope is a saturated determinantal ideal that gives rise to a new
model for the realization space of the polytope. The simplest slack ideals are toric and have …

Abstract Recently Gouveia, Thomas and the authors introduced the slack realization space,
a new model for the realization space of a polytope. It represents each polytope by its slack …

In this paper we examine four different models for the realization space of a polytope: the
classical model, the Grassmannian model, the Gale transform model, and the slack variety …

Chapter 1 describes several models for the realization space of a polytope. These models
include the classical model, a model representing realizations in the Grassmannian, a new …

For any finite poset P, we introduce a homogeneous space as a quotient of the general
linear group. When P is a chain this quotient is a complete flag variety. Moreover, we provide …

We report on a re-implementation in C++ of the search for non-realizability certificates for
simplicial spheres in the form of positive Plücker trees [16]. On the one hand, this …