The minimal resolution conjecture

By extending the ideal generation conjecture, we formulate the minimal resolution conjecture for a sufficiently generic set of points in P^n, and we explicitely write out the conjectured valuesof the Betti numbers. We then relate the minimal resolution conjecture to the ideal generation conjecture and the Cohen-Macaulay type conjecture and we prove the minimal reolution conjecture for binom(d+n,n)-l points (0<l<n+1), for n+2 points, and for binom(d-1+n,n)+1 points. We also prove the Cohen-Macaulay type conjecture for s points, with n<s<binomial(2+n,n)+1. Finally, we recover information about the resolution of s-1 or s+1 poits from that of s points.