## Reduced Gorenstein codimension three subschemes of projective space

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- by Anthony V. Geramita and Juan C. Migliore
- Proc. Amer. Math. Soc.
**125**(1997), 943-950 - DOI: https://doi.org/10.1090/S0002-9939-97-03956-7
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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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## Bibliographic Information

**Anthony V. Geramita**- Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6; Dipartimento di Matematica, Universitá di Genova, Genova, Italia
- MR Author ID: 72575
- Email: tony@mast.queensu.ca, geramita@dima.unige.it
**Juan C. Migliore**- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 124490
- ORCID: 0000-0001-5528-4520
- Email: Juan.C.Migliore.1@nd.edu
- Received by editor(s): July 24, 1995
- Communicated by: Eric M. Friedlander
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 943-950 - MSC (1991): Primary 14M05, 14C05, 13D02
- DOI: https://doi.org/10.1090/S0002-9939-97-03956-7
- MathSciNet review: 1403128