  Let $A$ be a commutative Noetherian local ring with maximal ideal
$\mathfrak{m}$, and let $I$ be an ideal. The fiber cone is then an image of the
polynomial ring over the residue field $A/\mathfrak{m}$. The kernel of this map
is called the defining ideal, and it is natural to ask how to compute it. In
this paper, we provide a construction for the defining ideals of Cohen-Macaulay
fiber cones.
