In this paper we restrict ourselves to the study of the ideal I associated to at most n+1 general fat points in P^n : a quite classical subject. Section 2 contains the computation of the Hilbert function of I . In Section 3, after recalling the notion of splittable ideals as in [S. Eliahou and M. A. Kervaire, J. Algebra 129 (1990), we show that the ideal I associated to two fat points is a splittable ideal. This allows us to compute the Betti numbers of the ideal associated to I . Finally, in the last section it is shown that the ideal I associated to at most n+1 double points is a splittable ideal, by first determining a minimal system of generators for I .
Ideals of fat points and splittable ideals.
FATABBI, Giuliana
1995
Abstract
In this paper we restrict ourselves to the study of the ideal I associated to at most n+1 general fat points in P^n : a quite classical subject. Section 2 contains the computation of the Hilbert function of I . In Section 3, after recalling the notion of splittable ideals as in [S. Eliahou and M. A. Kervaire, J. Algebra 129 (1990), we show that the ideal I associated to two fat points is a splittable ideal. This allows us to compute the Betti numbers of the ideal associated to I . Finally, in the last section it is shown that the ideal I associated to at most n+1 double points is a splittable ideal, by first determining a minimal system of generators for I .I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
