Matroidal Cayley-Bacharach and independence/dependence of geometric properties of matroids

Abstract

We consider the relationship between a matroidal analogue of the degree a Cayley-Bacharach property (finite sets of points failing to impose independent conditions on degree a hypersurfaces) and geometric properties of matroids. If the matroid polytopes in question are nestohedra, we show that the minimal degree matroidal Cayley-Bacharach property denoted MC B (a) is determined by the structure of the building sets used to construct them. This analysis also applies for other degrees a. Also, it does not seem to affect the combinatorial equivalence class of the matroid polytope. INDEPENDENCE FROM GEOMETRY AND NESTOHEDRABased on the matroidal Cayley-Bacharach property MC B (a) of degree a, we define MC B (a) for a building set B (Definition 7.1 on p. 1044 of [21]).The motivation/connection to the