An iterative construction of Gorenstein ideals

Bocci, C.; Dalzotto, G.; Notari, R.; Spreafico, M.

doi:10.1090/S0002-9947-04-03521-4

An iterative construction of Gorenstein ideals
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by C. Bocci, G. Dalzotto, R. Notari and M. L. Spreafico PDF

Trans. Amer. Math. Soc. 357 (2005), 1417-1444 Request permission

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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