Consider a semigroup ring
BH= k[th∕h ∈ H] where t is a transcendental over an algebraically closed field k of
characteristic 0. Let T1(B) denote T1(B∕k,B) where T1(B∕k,−) is the upper
cotangent functor of Lichtenbaum and Schlessinger. Then T1(B) is a graded k-vector
space of finite dimension and B is said to be negatively graded if T1(B)+= 0. It is
known that a versal deformation T∕S of B∕k exists in the sense of Schlessinger,
where (S,mS) is a complete noetherian local k-algebra. We say that the formal
moduli space is unobstructed if S is a regular local ring. In this paper we restrict our
attention to the negatively graded semigroup rings. In this case we compute the
dimension of T1(B) and are thus able to determine which formal moduli spaces are
unobstructed.
