ACM sheaves on a nonsingular quadric hypersurface in $P^4_k$

Abstract

We prove that on a nonsingular quadric hypersurface Q in $P^4_k$ even CI liaison classes of ACM curves are in bijective correspondence with the stable equivalence classes (up to shift in degree) of maximal Cohen-Macaulay graded modules over the coordinate ring R of Q, which in turn, are in bijective correspondence with stable equivalence classes (up to shift in degree) of ACM sheaves on Q . In the situation of a nonsingular quadric hypersurface Q in $P^4_k$ work of Knorrer shows that there is a unique nonfree indecomposable MCM module over R. We also describe the ACM sheaf corresponding to this MCM module and give its cohomology table and its Hilbert polynomial.