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TitleOn a class of power ideals
Author(s) J. Backelin, A. Oneto
TypeArticle in Journal
AbstractAbstract In this paper we study the class of power ideals generated by the k n forms ( x_0 + ξ g_1 x_1 + + ξ g_n x_n )^( k − 1 ) d where ξ is a fixed primitive kth-root of unity and 0 ≤ g j ≤ k − 1 for all j. For k = 2 , by using a Z k n + 1 -grading on C [ x 0 , , x n ] , we compute the Hilbert series of the associated quotient rings via a simple numerical algorithm. We also conjecture the extension for k > 2 . Via Macaulay duality, those power ideals are related to schemes of fat points with support on the k n points [ 1 : ξ g_1 : : ξ g_n ] in P n . We compute Hilbert series, Betti numbers and Gröbner basis for these 0-dimensional schemes. This explicitly determines the Hilbert series of the power ideal for all k: that this agrees with our conjecture for k > 2 is supported by several computer experiments.
ISSN0022-4049
URL http://www.sciencedirect.com/science/article/pii/S0022404914002886
LanguageEnglish
JournalJournal of Pure and Applied Algebra
Volume219
Number8
Pages3158 - 3180
Year2015
Edition0
Translation No
Refereed No
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