# On the defining equations of tangent cones of numerical semigroup rings

*Abstract:*

Let H be a numerical semigroup minimally generated by a1<dots<ar. We show that if we bound the width wd(H):=ar-a1, then the Betti numbers of the tangent cone grmK[H] are bounded as well. We conjecture what these bounds are in terms of the width and we present evidence to support this. This is joint work with Juergen Herzog.