The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the sphere g-conjecture implies all enumerative consequences of its far reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s manifold g-c...

We describe the tangent space to the parameter variety of all artin level quotients of a polynomial ring in n variables having specified socle degree and type. When n = 2, we relate this variety to the family of secants of the rational normal curve. With additional numerical hypotheses, we prove a projective normality theorem for the parameter variety in its natural Plücker embedding. AMS subje...

Many famous graphs are edge-primitive, for example, the Heawood graph, the Tutte–Coxeter graph and the Higman–Sims graph. In this paper we systematically analyse edge-primitive and edge-quasiprimitive graphs via the O’Nan–Scott Theorem to determine the possible edge and vertex actions of such graphs. Many interesting examples are given and we also determine all G-edge-primitive graphs for G an ...