Details:
Title  On a class of power ideals  Author(s)  J. Backelin, A. Oneto  Type  Article in Journal  Abstract  Abstract 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 kthroot 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 0dimensional 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.  ISSN  00224049 
URL 
http://www.sciencedirect.com/science/article/pii/S0022404914002886 
Language  English  Journal  Journal of Pure and Applied Algebra  Volume  219  Number  8  Pages  3158  3180  Year  2015  Edition  0  Translation 
No  Refereed 
No 
