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ISSN 1088-6826(e) ISSN 0002-9939(p)

Reduced Gorenstein codimension three subschemes of projective space

Author(s): Anthony V. Geramita; Juan C. Migliore
Journal: Proc. Amer. Math. Soc. 125 (1997), 943-950.
MSC (1991): Primary 14M05, 14C05, 13D02
MathSciNet review: 1403128
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Abstract: It is known, from work of Diesel, which graded Betti numbers are possible for Artinian Gorenstein height three ideals. In this paper we show that any such set of graded Betti numbers in fact occurs for a reduced set of points in $\mathbb P^3$ , a stick figure in $\mathbb P^4$ , or more generally, a good linear configuration in $\mathbb P^n$ . Consequently, any Gorenstein codimension three scheme specializes to such a ``nice'' configuration, preserving the graded Betti numbers in the process. This is the codimension three Gorenstein analog of a classical result of arithmetically Cohen-Macaulay codimension two schemes.

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