Vol. 82, No. 1, 1979

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The obstruction of the formal moduli space in the negatively graded case

Marie Angela Vitulli

Vol. 82 (1979), No. 1, 281–294

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.

Mathematical Subject Classification 2000
Primary: 14B07
Received: 7 November 1977
Published: 1 May 1979
Marie Angela Vitulli