Even Linkage Classes

Abstract

In this paper the author generalizes the $\E$ and $\N$-type resolutions used by Martin-Deschamps and Perrin 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 $\E$ satisfying $H^1_*(\E)=0$ and $\ext^1(\E^\vee, \O)=0$. Further, these resolutions are used to extend the work of Martin-Deschamps and Perrin for Cohen-Macaulay curves in $\Pthree$ to subschemes of pure codimension two in $\Pn$. In particular, even linkage classes of such subschemes have the Lazarsfeld-Rao property and any minimal subscheme for an even linkage class is directly linked to a minimal subscheme for the dual class.