Distractions of Shakin rings

JOURNAL OF ALGEBRA

卷:419

Article

Caviglia, Giulio¹  Sbarra, Enrico² 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

关键词: Eisenbud-Green-Harris Conjecture;    Embeddings of Hilbert functions;    Distractions;    Piecewise lex-segment ideals;   

DOI  :  10.1016/j.jalgebra.2014.05.008

来源: Elsevier

【 摘 要 】

We study, by means of embeddings of Hilbert functions, a class of rings which we call Shakin rings, i.e. quotients K[X-1, . . . , X-n]/a of a polynomial ring over a field K by ideals a = L + P which are the sum of a piecewise lex-segment ideal L, as defined by Shakin, and a pure powers ideal P. Our main results extend Abedelfatah's recent work on the Eisenbud-Green-Harris Conjecture, Shakin's generalization of Macaulay and Bigatti-Hulett-Pardue Theorems on Betti numbers and, when char(K) = 0, Mermin-Murai Theorem on the Lex-Plus-Power inequality, from monomial regular sequences to a larger class of ideals. We also prove an extremality property of embeddings induced by distractions in terms of Hilbert functions of local cohomology modules. (C) 2014 Published by Elsevier Inc.

【 授权许可】

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