## Illinois Journal of Mathematics

### A characterization of the Macaulay dual generators for quadratic complete intersections

#### 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 $B\subset A(F)$ 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.

#### Article information

Source
Illinois J. Math., Volume 61, Number 3-4 (2017), 371-383.

Dates
Revised: 23 May 2018
First available in Project Euclid: 22 August 2018

https://projecteuclid.org/euclid.ijm/1534924831

Digital Object Identifier
doi:10.1215/ijm/1534924831

Mathematical Reviews number (MathSciNet)
MR3845725

Zentralblatt MATH identifier
06932508

#### Citation

Harima, Tadahito; Wachi, Akihito; Watanabe, Junzo. A characterization of the Macaulay dual generators for quadratic complete intersections. Illinois J. Math. 61 (2017), no. 3-4, 371--383. doi:10.1215/ijm/1534924831. https://projecteuclid.org/euclid.ijm/1534924831

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