  Our results concern minimal graded free resolutions of fat point ideals for
points in a hyperplane. Suppose, for example, that I(m,d) is the ideal defining
r given points of multiplicity m in the projective space P^d. Assume that the
given points lie in a hyperplane P^{d-1} in P^d, and that the ground field k is
algebraically closed of characteristic 0. We give an explicit minimal graded
free resolution of I(m,d) in k[P^d] in terms of the minimal graded free
resolutions of the ideals I(j,d-1) in k[P^{d-1}] with j < m+1. As a corollary,
we give the following formula for the Poincare polynomial P_{m,d} of I(m,d) in
terms of the Poincare polynomials P_{j,d-1} of I(j,d-1): P_{m,d} = (1 +
XT)(\Sigma_{0<j\le m} T^{m-j}(P_{j,d-1} - 1)) + 1 + XT^m.
