A CHARACTERIZATION OF THE MACAULAY DUAL GENERATORS FOR QUADRATIC COMPLETE INTERSECTIONS

摘要

Let F be a homogeneous polynomial in n variables of degree d over a field K. Let A(F) be the associated Artinian graded K-algebra. If B ⊂ A(F) is a subalgebra of A(F) which is Gorenstein with the same socle degree as A(F), we describe the Macaulay dual generator for B in terms of F. Furthermore when n = d, we give necessary and sufficient conditions on the polynomial F for A(F) to be a complete intersection.