Distractions of Shakin rings

作者：Caviglia Giulio^*; Sbarra Enrico

来源：Journal of Algebra, 2014, 419: 318-331.

DOI：10.1016/j.jalgebra.2014.05.008

• Eisenbud-Green-Harris Conjecture
• Embeddings of Hilbert functions
• Distractions
• Piecewise lex-segment ideals

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%26apos;s recent work on the Eisenbud-Green-Harris Conjecture, Shakin%26apos;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.

• 出版日期2014-12-1