Illinois Journal of Mathematics

A characterization of the Macaulay dual generators for quadratic complete intersections

Tadahito Harima, Akihito Wachi, and Junzo Watanabe

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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

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

Received: 22 March 2017
Revised: 23 May 2018
First available in Project Euclid: 22 August 2018

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Zentralblatt MATH identifier

Primary: 13A02: Graded rings [See also 16W50] 13C11: Injective and flat modules and ideals 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13M10: Polynomials


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.

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