Generic Quotients of Level Algebras of Arbitrary Type

Let A be a type t artinian level algebra with h-vector h =) be the h-vector of the generic type c level quotient of A having the same socle degree e. The main result of this paper is an (in general sharp) lower-bound for the h-vector H H c,gen u ≥ 1 t 2 − 1 ((t − c)h e−u + (ct − 1)h u). This result generalizes a recent theorem of Iarrobino (which treats the case t = 2). Finally, we begin to obtain, as a consequence, some structure theorems for level h-vectors of type bigger than 2, which is, at this time, a very little explored topic.