  Call a monomial ideal M "generic" if no variable appears with the same
nonzero exponent in two distinct monomial generators. Using a convex polytope
first studied by Scarf, we obtain a minimal free resolution of M. Any monomial
ideal M can be made generic by deformation of its generating exponents. Thus,
the above construction yields a (usually nonminimal) resolution of M for
arbitrary monomial ideals, bounding the Betti numbers of M in terms of the
Upper Bound Theorem for Convex Polytopes.
  We show that our resolutions are DG-algebras, and consider realizability
questions and irreducible decompositions.
