A characterization of the Macaulay dual generators for quadratic complete intersections

2017/03/21 by Harima, Tadahito, Wachi, Akihito, Watanabe, Junzo
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.07199

Abstract

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.

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