Geometric domains with specified pseudo-dimensions

This paper pursues the study of the pseudo-supports of a finitely generated module over a finite-dimensional commutative Noetherian ring, and is particularly concerned with the properties of the pseudo-supports of a geometric normal local domain. It is shown that these pseudo-supports have certain properties that can be summarized by the so-called occurrence diagram of the ring, which is a certain subset of . Standard properties of local cohomology modules enable one to conclude that there are obvious restrictions on the type of subset of that can be an occurrence diagram in this way, and much of the paper is devoted to consideration of whether a subset of that meets those obvious restrictions is an occurrence diagram of some geometric normal local domain. These occurrence diagrams are also used to assist with the production of examples that show that a question raised by C. Huneke, about certain sets related to Grothendieckʹs Finiteness Theorem for local cohomology, has a negative answer.