Ideal containments under flat extensions

JOURNAL OF ALGEBRA

卷:492

Article

关键词: Symbolic powers;    Fat points;    Points in the projective plane;    Fermat configuration;    Regular sequences;    Cohen-Macaulay;    Algebraic geometry;    Commutative algebra;   

DOI  :  10.1016/j.jalgebra.2017.07.026

来源: Elsevier

【 摘 要 】

Let phi : S = k[y(0),...y(n)] -> R = k[y(0),...y(n)] be given by y(i) -> f(i) where f(0),... f(n) is an R-regular sequence of homogeneous elements of the same degree. A recent paper shows for ideals, I-Delta subset of S, of matroids, Delta, that I-Delta((m)) subset of I-r if and only if phi*(I-Delta)((m)) subset of phi(I-Delta)(r) where phi*(I-Delta) is the ideal generated in R by phi(I-Delta). We prove this result for saturated homogeneous ideals I of configurations of points in P-n and use it to obtain many new counterexamples to I(rn-n+1) phi(I-Delta) I-r from previously known counterexamples. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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