  We consider the minimal free resolution of a generic set of n+1 forms (not
necessarily of the same degree) in a polynomial ring of n variables. The
Hilbert function for such an ideal is known, thanks to a result of Stanley and
of Watanabe. (For more than n+1 forms the Hilbert function is conjectured by
Froberg.) However, in all but a few trivial cases, the resolution is not known.
A conjecture of Iarrobino says that apart from Koszul syzygies, there should be
no overlaps in the twists occurring in the free modules in the resolution. We
are able to find the precise minimal free resolutions in many cases (depending
on n and on the particular degrees) and give good bounds in many other cases.
As a result, we see that Iarrobino's conjecture does not hold and we begin to
have an understanding of what causes this failure. We conjecture that there are
no such overlaps when all n+1 generators have the same degree. In the process
of achieving these results, we extend a result of Boij by giving the graded
Betti numbers of a generic Gorenstein algebra when n is even and the socle
degree is large.
