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A construction of codimension three arithmetically Gorenstein subschemes of projective space


Authors: Juan C. Migliore and Chris Peterson
Journal: Trans. Amer. Math. Soc. 349 (1997), 3803-3821
MSC (1991): Primary 14F05, 14M05; Secondary 14M06, 14M07, 13D02
DOI: https://doi.org/10.1090/S0002-9947-97-01978-8
MathSciNet review: 1432204
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Abstract: This paper presents a construction method for a class of codimension three arithmetically Gorenstein subschemes of projective space. These schemes are obtained from degeneracy loci of sections of certain specially constructed rank three reflexive sheaves. In contrast to the structure theorem of Buchsbaum and Eisenbud, we cannot obtain every arithmetically Gorenstein codimension three subscheme by our method. However, certain geometric applications are facilitated by the geometric aspect of this construction, and we discuss several examples of this in the final section.


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Additional Information

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

Chris Peterson
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: peterson@math.nd.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01978-8
Keywords: Rank three reflexive sheaves, codimension three schemes, arithmetically Gorenstein, linkage, liaison, Buchsbaum-Rim complex
Received by editor(s): April 30, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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