Horrocks Correspondence on ACM Varieties

الأصل · EN

We describe a vector bundle on a smooth n-dimensional ACM variety in terms of its cohomological invariants Hⁱ*(), 1≤ i ≤ n-1, and certain graded modules of "socle elements" built from. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in Pⁿ⁺¹ and the Veronese surface in P⁵ are considered in more detail.