Illinois Journal of Mathematics

Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials

Toshiaki Maeno and Junzo Watanabe

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Abstract

We give a characterization of the Lefschetz elements in Artinian Gorenstein rings over a field of characteristic zero in terms of the higher Hessians. As an application, we give new examples of Artinian Gorenstein rings which do not have the strong Lefschetz property.

Article information

Source
Illinois J. Math., Volume 53, Number 2 (2009), 591-603.

Dates
First available in Project Euclid: 23 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1266934795

Digital Object Identifier
doi:10.1215/ijm/1266934795

Mathematical Reviews number (MathSciNet)
MR2594646

Zentralblatt MATH identifier
1200.13031

Subjects
Primary: 13E10: Artinian rings and modules, finite-dimensional algebras
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Citation

Maeno, Toshiaki; Watanabe, Junzo. Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials. Illinois J. Math. 53 (2009), no. 2, 591--603. doi:10.1215/ijm/1266934795. https://projecteuclid.org/euclid.ijm/1266934795


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