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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reduced Gorenstein codimension three
subschemes of projective space


Authors: Anthony V. Geramita and 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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Additional 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
Email: tony@mast.queensu.ca, geramita@dima.unige.it

Juan C. Migliore
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: Juan.C.Migliore.1@nd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03956-7
PII: S 0002-9939(97)03956-7
Received by editor(s): July 24, 1995
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1997 American Mathematical Society