  We construct explicitly regular sequences in the semigroup ring $R=\CC[K]$ of
lattice points of the graded cone $K$. We conjecture that the quotients of $R$
by these sequences describe locally string-theoretic cohomology of a toroidal
singularity associated to $K$. As a byproduct, we give an elementary proof of
the result of Hochster that semigroup rings of rational polyhedral cones are
Cohen-Macaulay.

Algebraic Geometry;Commutative Algebra