Type cones and products of simplices

Abstract: A polytope $P$ is the convex hull of finitely many points in Euclidean space. For polytopes $P$ and $Q$, we say that $Q$ is a Minkowski summand of $P$ if there exists some polytope $R$ such that $Q+R=P$. The type cone of $P$ encodes all of the (weak) Minkowski summands of P. In general, combinatorially isomorphic polytopes can have different type cones. We will first consider type cones of polygons, and then show that if $P$ is combinatorially isomorphic to a product of simplices, then the type cone is simplicial. This is joint work with Federico Castillo, Joseph Doolittle, Michael Ross, and Li Ying.

commutative algebraalgebraic geometrycombinatorics

Audience: researchers in the topic

Matroids - Combinatorics, Algebra and Geometry Seminar