We give information on the Hilbert function of a Cohen-Macaulay idealI of the polynomial ring R=k[x_0 , x_1 , ..., x_r] which is minimally generatedby t forms of degrees d_1 ,... , d_t. Mainly we deal with the codimension twocase in which we show that the Dubreil bound t<=d_1+1 is a necessary andsufficient condition to have such an ideal and we give a sharp upper bound andlower bound for the Hilbert function. In codimension greater than two we givea characterization for having such an ideal and in codimension 3 we find anHilbert function which is maximal for these ideals with d_1=...=d_t=a andwe produce a scheme which realizes such a Hilbert function.
Hilbert functions of Cohen Macaulay ideals with assigned generators' degrees Rend. Univ. Padova
RAGUSA, Alfio;ZAPPALA', Giuseppe
2004-01-01
Abstract
We give information on the Hilbert function of a Cohen-Macaulay idealI of the polynomial ring R=k[x_0 , x_1 , ..., x_r] which is minimally generatedby t forms of degrees d_1 ,... , d_t. Mainly we deal with the codimension twocase in which we show that the Dubreil bound t<=d_1+1 is a necessary andsufficient condition to have such an ideal and we give a sharp upper bound andlower bound for the Hilbert function. In codimension greater than two we givea characterization for having such an ideal and in codimension 3 we find anHilbert function which is maximal for these ideals with d_1=...=d_t=a andwe produce a scheme which realizes such a Hilbert function.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.