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Powers of generic ideals and the weak Lefschetz property for powers of some monomial complet intersections
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32018 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 495, p. 1-14Article in journal (Refereed) Published
Abstract [en]

Given an ideal I = (f(1) ... , f(r)) in C[x(1), ... , x(n),] generated by forms of degree d, and an integer k > 1, how large can the ideal I-k be, i.e., how small can the Hilbert function of C[x(1), ... , x(n)] / I-k be? If r <= n the smallest Hilbert function is achieved by any complete intersection, but for r > n, the question is in general very hard to answer. We study the problem for r = n + 1, where the result is known for k = 1. We also study a closely related problem, the Weak Lefschetz property, for S/I-k, where I is the ideal generated by the d'th powers of the variables.

Place, publisher, year, edition, pages
2018. Vol. 495, p. 1-14
Keywords [en]
Generic forms, Weak Lefschetz property, Hilbert series, Froberg's conjecture
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-151170DOI: 10.1016/j.jalgebra.2017.11.001ISI: 000418106900001OAI: oai:DiVA.org:su-151170DiVA, id: diva2:1179542
Available from: 2018-02-01 Created: 2018-02-01 Last updated: 2018-02-01Bibliographically approved

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