Função de Hilbert e suas conexões com outros invariantes

Abstract

An important invariant associated with a graded module is the Hilbert function. Through it other invariants arise, such as the polynomial and the Hilbert series. A notable fact about these three concepts is that they relate to various other information of the graded module, the example of the Krull dimension, multiplicity, graded free resolution, etc. In this work of dissertation our objective is to study properties of the function, the polynomial and the Hilbert series as well as presenting the connection of these concepts with others like those already mentioned.