GORENSTEIN ALGEBRAS OF VERONESE TYPE

Let K[t(1),t(2),..., t(n)] be the polynomial ring in n variables over a field K. We fix an integer d and a sequence a = (a(1), a(2),..., a(n )) of integers with 1 less than or equal to a(1) less than or equal to a(2) less than or equal to ... less than or equal to a(n) less than o r equal to d and d < Sigma(i=1)(n) a(i). Let A(a; d) denote the K-suba lgebra of K[t(1), t(2),..., t(n)] generated by all monomials of the fo rm t(1)(x1)t(2)(x2) ... t(n)(xn) with x(1) + x(2) + ... +x(n) = d and with x(i) less than or equal to a(i) for each 1 less than or equal to i less than or equal to n. In this paper we classify all the sequences a and integers d for which the algebra A(a; d) is Gorenstein. (C) 199 7 Academic Press.