## Even Linkage Classes

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- by Scott Nollet PDF
- Trans. Amer. Math. Soc.
**348**(1996), 1137-1162 Request permission

## 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 $\mathcal {E}xt^{1}( \mathcal {E}^{\vee }, \mathcal {O})=0$. 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.## References

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## Additional Information

**Scott Nollet**- Affiliation: 2919 Fulton St., Berkeley, California 94705
- MR Author ID: 364618
- Email: nollet@math.berkeley.edu
- Received by editor(s): March 6, 1995
- © Copyright 1996 American Mathematical Society
- 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