Gorenstein Algebras of Veronese Type Original Research Article

LetK[t1, t2,…,tn] be the polynomial ring innvariables over a fieldK. We fix an integerdand a sequencea = (a1, a2,…,an) of integers with 1 ≤ a1 ≤ a2 ≤ ··· ≤ an ≤ dandimage. LetA(a; d) denote theK-subalgebra ofK[t1, t2,…,tn] generated by all monomials of the formt1x1t2x2···tnxnwithx1 + x2 + ··· + xn = dand withxi ≤ aifor each 1 ≤ i ≤ n. In this paper we classify all the sequencesaand integersdfor which the algebraA(a; d) is Gorenstein.