Numerical semigroups with multiplicity $m$ are parameterized by integer points in a polyhedral cone $C_m$, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall structure is identical for all semigroups parametrized by the relative interior of a fixed face of $C_m$. This resolution is minimal when the semigroup is maximal embedding dimension, which is the case parametrized by the interior of $C_m$ itself. This resolution is employed to show uniformity of Betti numbers for all toric ideals defined by semigroups parametrized by points interior to a single face of $C_m$.
Comment: 19 pages