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Powers of generic ideals and the weak Lefschetz property for powers of some monomial complete intersections
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-9961-383X
2018 (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=(f1,…,fr) in C[x1,…,xn] generated by forms of degree d, and an integer k>1, how large can the ideal Ik be, i.e., how small can the Hilbert function of C[x1,…,xn]/Ik 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/Ik, where I is the ideal generated by the d'th powers of the variables.

Place, publisher, year, edition, pages
Academic Press, 2018. Vol. 495, p. 1-14
Keywords [en]
Fröberg's conjecture, Generic forms, Hilbert series, Weak Lefschetz property
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-218917DOI: 10.1016/j.jalgebra.2017.11.001Scopus ID: 2-s2.0-85033590818OAI: oai:DiVA.org:kth-218917DiVA, id: diva2:1161864
Note

QC 20171201

Available from: 2017-12-01 Created: 2017-12-01 Last updated: 2017-12-01Bibliographically approved

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Boij, Mats

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