Even Linkage Classes
Author:
Scott Nollet
Journal:
Trans. Amer. Math. Soc. 348 (1996), 1137-1162
MSC (1991):
Primary 14M06; Secondary 14M12, 13C40
DOI:
https://doi.org/10.1090/S0002-9947-96-01552-8
MathSciNet review:
1340182
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we generalize the and
-type resolutions used by Martin-Deschamps and Perrin for curves in
to subschemes of pure codimension in projective space, and shows that these resolutions are interchanged by the mapping cone procedure under a simple linkage. Via these resolutions, Rao's correspondence is extended to give a bijection between even linkage classes of subschemes of pure codimension two and stable equivalence classes of reflexive sheaves
satisfying
and
. Further, these resolutions are used to extend the work of Martin-Deschamps and Perrin for Cohen-Macaulay curves in
to subschemes of pure codimension two in
. In particular, even linkage classes of such subschemes satisfy the Lazarsfeld-Rao property and any minimal subscheme for an even linkage class links directly to a minimal subscheme for the dual class.
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Additional Information
Scott Nollet
Affiliation:
2919 Fulton St., Berkeley, California 94705
Email:
nollet@math.berkeley.edu
DOI:
https://doi.org/10.1090/S0002-9947-96-01552-8
Keywords:
Even linkage classes,
Lazarsfeld-Rao property,
Rao's correspondence
Received by editor(s):
March 6, 1995
Article copyright:
© Copyright 1996
American Mathematical Society