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Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen-Macaulay case
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-9961-383X
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2012 (English)In: Algebra & Number Theory, ISSN 1937-0652, E-ISSN 1944-7833, Vol. 6, no 3, 437-454 p.Article in journal (Refereed) Published
Abstract [en]

We use results of Eisenbud and Schreyer to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination of Betti diagrams of modules with a pure resolution. This implies the multiplicity conjecture of Herzog, Huneke, and Srinivasan for modules that are not necessarily Cohen-Macaulay and also implies a generalized version of these inequalities. We also give a combinatorial proof of the convexity of the simplicial fan spanned by pure diagrams.

Place, publisher, year, edition, pages
2012. Vol. 6, no 3, 437-454 p.
Keyword [en]
graded modules, Betti numbers, multiplicity conjecture
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-100179DOI: 10.2140/ant.2012.6.437ISI: 000306191600002Scopus ID: 2-s2.0-84863800231OAI: oai:DiVA.org:kth-100179DiVA: diva2:542930
Note
QC 20120806Available from: 2012-08-06 Created: 2012-08-06 Last updated: 2017-12-07Bibliographically approved

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Boij, Mats

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