In this paper basic facts will be introduced, the use of fruitful techniques will be stressed in order to present easier proofs of known facts and to get a taste of some open problems. Start- ing from classical results by S. Abhyankar, D. Northcott and J. Sally, we present results on the coefficients of the Hilbert Polynomial and, in several cases, we discuss algebraic and geometric properties of the local ring in terms of this asymptotic information. The paper ends with results and techniques concerning the Hilbert function of Artinian Gorenstein local k-algebras.
Hilbert Functions of Cohen-Macaulay local rings
ROSSI, MARIA EVELINA
2011-01-01
Abstract
In this paper basic facts will be introduced, the use of fruitful techniques will be stressed in order to present easier proofs of known facts and to get a taste of some open problems. Start- ing from classical results by S. Abhyankar, D. Northcott and J. Sally, we present results on the coefficients of the Hilbert Polynomial and, in several cases, we discuss algebraic and geometric properties of the local ring in terms of this asymptotic information. The paper ends with results and techniques concerning the Hilbert function of Artinian Gorenstein local k-algebras.
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