An iterative construction of Gorenstein ideals
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY(2005)
Abstract
In this paper, we present a method to inductively construct Gorenstein ideals of any codimension c. We start from a Gorenstein ideal I of codimension c contained in a complete intersection ideal J of the same codimension, and we prove that under suitable hypotheses there exists a new Gorenstein ideal contained in the residual ideal I : J. We compare some numerical data of the starting and the resulting Gorenstein ideals of the construction. We compare also the Buchsbaum-Eisenbud matrices of the two ideals, in the codimension three case. Furthermore, we show that this construction is independent from the other known geometrical constructions of Gorenstein ideals, providing examples.
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Key words
gorenstein ideals,iterative construction
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