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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Even Linkage Classes


Author: Scott Nollet
Journal: Trans. Amer. Math. Soc. 348 (1996), 1137-1162
MSC (1991): Primary 14M06; Secondary 14M12, 13C40
MathSciNet review: 1340182
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Abstract: In this paper we generalize the $ \mathcal{E}$ and $ \mathcal{N}$-type resolutions used by Martin-Deschamps and Perrin for curves in $ \mathbb{P}^{3}$ 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 $ \mathcal{E}$ satisfying $H^{1}_{*}( \mathcal{E})=0$ and $ \mathop{\mathcal{E}xt}^{1}( \mathcal{E}^{\vee }, \mathcal{O})=0$. Further, these resolutions are used to extend the work of Martin-Deschamps and Perrin for Cohen-Macaulay curves in $ \mathbb{P}^{3}$ to subschemes of pure codimension two in $ \mathbb{P}^{n}$. 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