Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen-Macaulay case
2012 (English)In: Algebra & Number Theory, ISSN 1937-0652, Vol. 6, no 3, 437-454 p.Article in journal (Refereed) Published
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.
graded modules, Betti numbers, multiplicity conjecture
IdentifiersURN: urn:nbn:se:kth:diva-100179DOI: 10.2140/ant.2012.6.437ISI: 000306191600002ScopusID: 2-s2.0-84863800231OAI: oai:DiVA.org:kth-100179DiVA: diva2:542930
QC 201208062012-08-062012-08-062012-08-06Bibliographically approved