Two-dimensional orders of finite representation type.
The goal of this paper is to develop tools to study maximal families of Gorenstein quotients A of a polynomial ring R. We prove a very general theorem on deformations of the homogeneous coordinate ring of a scheme Proj(A) which is defined as the degeneracy locus of a regular section of the dual of some sheaf M of rank r supported on say an arithmetically Cohen-Macaulay subscheme Proj(B) of Proj(R). Under certain conditions (notably; M maximally Cohen-Macaulay and ∧r M ≈ KB(t) a twist of the canonical...
We show that the -signature of an -finite local ring of characteristic exists when is either the localization of an -graded ring at its irrelevant ideal or -Gorenstein on its punctured spectrum. This extends results by Huneke, Leuschke, Yao and Singh and proves the existence of the -signature in the cases where weak -regularity is known to be equivalent to strong -regularity.