Details:
Title  On the Hilbert function of onedimensional local complete intersections  Author(s)  Juan Elias, M.E. Rossi, G. Valla  Type  Article in Journal  Abstract  Abstract The sequences that occur as Hilbert functions of standard graded algebras A are well understood by Macaulayʼs theorem; those that occur for graded complete intersections are elementary and were known classically. However, much less is known in the local case, once the dimension of A is greater than zero, or the embedding dimension is three or more. Using an extension to the power series ring R of Gröbner bases with respect to local degree orderings, we characterize the Hilbert functions H of onedimensional quadratic complete intersections A = R / I , I = ( f , g ) , of type ( 2 , 2 ) that is, that are quotients of the power series ring R in three variables by a regular sequence f, g whose initial forms are linearly independent and of degree 2. We also give a structure theorem up to analytic isomorphism of A for the minimal system of generators of I, given the Hilbert function. More generally, when the type of I is ( 2 , b ) we are able to give some restrictions on the Hilbert function. In this case we can also prove that the associated graded algebra of A is Cohen–Macaulay if and only if the Hilbert function of A is strictly increasing.  Keywords  Onedimensional local rings, Hilbert functions, Complete intersections  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869313005620 
Language  English  Journal  Journal of Algebra  Volume  399  Pages  489  515  Year  2014  Edition  0  Translation 
No  Refereed 
No 
