Transactions of the American Mathematical Society

A construction of codimension three arithmetically Gorenstein subschemes of projective space

Author(s): Juan C. Migliore; Chris Peterson
Journal: Trans. Amer. Math. Soc. 349 (1997), 3803-3821.
MSC (1991): Primary 14F05, 14M05; Secondary 14M06, 14M07, 13D02
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 14F05, 14M05, 14M06, 14M07, 13D02

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: 10.1090/S0002-9947-97-01978-8
PII: S 0002-9947(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
Copyright of article: Copyright 1997, American Mathematical Society

A. Kustin, The minimal free resolution of the Migliore-Peterson rings in the case that the reflexive sheaf has even rank, J. Algebra 207 (1998), 572-615.

J. Migliore, U. Nagel and C. Peterson, Buchsbaum-Rim sheaves and their multiple sections, J. Algebra 219 (1999), 378-420.

J. Migliore, Introduction to Liaison Theory and Deficiency Modules, Progress in Mathematics, vol. 165, Birkhauser, 1998.

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