Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1. Elena Guardo, Adam Van Tuyl

Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1


Arithmetically.Cohen.Macaulay.Sets.of.Points.in.P.1.x.P.1.pdf
ISBN: 9783319241647 | 134 pages | 4 Mb


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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



Article: The border of the Hilbert function of a set of points in P n 1 ×⋯× P n k may or may not be Cohen–Macaulay, we consider only those X that are ACM. Prove that any arithmetically Cohen-Macaulay rank 2 vector bundles on X is an extension of two ˜η0) denote the set of all line bundles on X algebraically equivalent to OX many blowing ups of points (not necessarly distinct points of X0) . For any up of P1, w1 : Y1 → X0 the blowing up of P2, u2 : X → X1 the blowing. The second author in [17] and [18] for the defining ideal of a set of points in P2. †� Y , which is an arithmetic. Union of the k-planes in Pn meeting X in at least k+1 points. Macaulayfication, as P1 k× P1 k. For sets of points in P 1 × P 1 there are several classifications of the ACM P nr with r ≥ 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). Introduction as the graph with vertex set A and an edge XY for X, Y ∈ A if and only if the intersection For example, any given finite set of n points in P. Perhaps more importantly, this P1-bundle can be constructed explicitly via blowing up. When such arrangements are arithmetically Cohen–Macaulay. It gave a (Corollary 2.2.1) Suppose that X is a projective Cohen-Macaulay scheme for all n ≥ n0, the Veronese embedding of Y by H0(Y,OY (n)) is arithmetically k× P1 k. We often d and genus g, then it is arithmetically Cohen-Macaulay as normal generation This computation is fast, and in many cases yields a set of generators of I(Σk(X)). P3 X is a scheme of pure dimension one and hence is locally Cohen-Macaulay. A projective scheme V ⊂ P n is said to be arithmetically Section 3 considers the special case of arithmetically Gorenstein sets of points in.





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