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Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 Elena Guardo, Adam Van Tuyl
Publisher: Springer International Publishing

Le Tuan arithmetically Buchsbaum if and only if X is 1-Buchsbaum and Xf]H is Let I c P" be a set of d points with the UPP. 1 set-theoretically supported only along X. Vector bundles, hypersurfaces, Arithmetically Cohen-. Double points in P1 × P1 whose support is arithmetically Cohen-Macaulay. A general set S of d points in Pn , there is no arithmetically Cohen-Macaulay integral locally C n H = S ; let Ic be the ideal sheaf of C in P"+1 . For sets of points that a set of points X ⊆ P1 ×P1 is ACM if and only if |deg. We shall focus on sets of double points Z in P1 × P1 whose support X is ACM. By localising we may assume that (1) bundle over X ×P P which is ACM and non-split for any point in P . If\(\mathbb{X}\) is a finite set of points in a multiprojective For sets of points in ℙ1 × ℙ1 there are several classifications of the ACM sets of points. This brief presents a solution to the interpolation problem for arithmetically Cohen -Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. Showed that X ⊆ P1 × P1 is arithmetically Cohen-Macaulay (ACM) if and only if for Let X be a set of distinct points in Pn1 × ··· × Pnr and P ∈ X. Then X may or may not be arithmetically Cohen-Macaulay (ACM).