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Lech's inequality, the Stuckrad-Vogel conjecture, and uniform behavior of Koszul homology
Stockholm University, Faculty of Science, Department of Mathematics.
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Number of Authors: 52019 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 347, p. 442-472Article in journal (Refereed) Published
Abstract [en]

Let (R, m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. We prove that the set {l(M/IM)/e(I, M)}(root I=m) is bounded below by 1/d!e((R) over bar) where (R) over bar = R/ Ann(M). Moreover, when (M) over cap is equidimensional, this set is bounded above by a finite constant depending only on M. The lower bound extends a classical inequality of Lech, and the upper bound answers a question of Stuckrad-Vogel in the affirmative. As an application, we obtain results on uniform behavior of the lengths of Koszul homology modules.

Place, publisher, year, edition, pages
2019. Vol. 347, p. 442-472
Keywords [en]
Hilbert-Samuel multiplicities, Lech's inequality, Koszul homology, Stuckrad-Vogel conjecture
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-168326DOI: 10.1016/j.aim.2019.02.029ISI: 000464091600009OAI: oai:DiVA.org:su-168326DiVA, id: diva2:1317304
Available from: 2019-05-22 Created: 2019-05-22 Last updated: 2019-05-22Bibliographically approved

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