Apery and micro-invariants of a one dimensional Cohen-Macaulay local ring and invariants of its tangent cone

Abstract

Given a one-dimensional Cohen-Macaulay local ring we compare several sets of invariants (micro-invariants, Apery invariants and invariants of the tangent cone) and give explicit formulas relating them. We show that, in fact, they coincide if and only if the tangent cone of the ring is Cohen-Macaulay. Some explicit computations are also given, particularly in the case of semigroup rings.