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

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



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Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 Elena Guardo, Adam Van Tuyl ebook
Publisher: Springer International Publishing
ISBN: 9783319241647
Page: 134
Format: pdf


P is called an essential multi-index for M. X ∈ N \ {0} induces an operator of degree 1 on Ma. For sets of points in P1 × P1 there are several classifications of the ACM sets of points. And give a complete description of the arithmetically Cohen-Macaulay. 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. The set es(M) of all essential multi- indices is a polytope P(M) ⊂ RN such that the lattice points S(M) in P(M) are exactly es(M). O- dimensional tion is to investigate O-dimensional subschemes of a quadric (P1 x P1) with special A very naive question arises at this point: given a set of points X. For a finite set of points X⊆Pn and for a given point P∈X, the notion of a Article : Separators of Arithmetically Cohen-Macaulay fat points in P^1 x P^1. If X is a finite set of points in a multiprojective space P^{n_1} × · · · × P^{n_r} with r ≥ 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). Arithmetically Cohen-Macaulay varieties. In numerical algebraic geometry, a witness point set W is a key object for performing deciding if X is arithmetically Cohen-Macaulay using points which ( approximately) lie on the point in Cn+1 corresponding to ̂c in V(p).





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