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On a class of power ideals
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2015 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, no 8, 3158-3180 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the class of power ideals generated by the k(n) forms (x(0) + xi(g1) x(1) + ... + xi(gn) x(n))((k-1)d) where xi 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 : xi(g1) : ... : xi(gn)] in P-n. We compute Hilbert series, Betti numbers and Grobner 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.

Place, publisher, year, edition, pages
2015. Vol. 219, no 8, 3158-3180 p.
Keyword [en]
Power Ideals, Fat Points, Hilbert function
National Category
Algebra and Logic Geometry
Identifiers
URN: urn:nbn:se:su:diva-111885DOI: 10.1016/j.jpaa.2014.10.007ISI: 000351979000004OAI: oai:DiVA.org:su-111885DiVA: diva2:777022
Available from: 2015-01-08 Created: 2015-01-08 Last updated: 2017-12-05Bibliographically approved

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