We study a variety for graded maximal Cohen–Macaulay modules, which was introduced by Dao and Shipman. The main result of this paper asserts that there are only finite number isomorphism classes modules with fixed Hilbert series over algebras countable representation type.

If a pure simplicial complex is partitionable, then its h-vector has combinatorial interpretation in terms of any partitioning the complex. Given non-partitionable Δ, we construct Γ⊇Δ same dimension such that both Γ and relative (Γ,Δ) are partitionable. This allows us to rewrite as difference two h-vectors partitionable complexes, giving an analogous By contrast, for given Δ it not always possi...