Convex Geometry of Building Sets

Building sets were introduced in the study of wonderful compactifications of hyperplane arrangement complements and were later generalized to meet-semilattices. Convex geometries, the duals of antimatroids, offer a robust combinatorial abstraction of convexity. Supersolvable convex geometries and antimatroids make appearances in the study of poset closure operators, Coxeter groups, and matroid activities. We prove that the building sets on a meet-semilattice form a supersolvable convex geometry.