Betti numbers of Z(n)-graded modules

Autor(en): Brun, M
Romer, T 
Stichwörter: Betti numbers; BOUNDS; COHOMOLOGY; FREE RESOLUTIONS; koszul homology; lower bounds; Mathematics
Erscheinungsdatum: 2004
Herausgeber: MARCEL DEKKER INC
Journal: COMMUNICATIONS IN ALGEBRA
Volumen: 32
Ausgabe: 12
Startseite: 4589
Seitenende: 4599
Zusammenfassung: 
Let S = K[X-1,..., X-n] be the polynomial ring over a field K. For bounded below Z(n)-graded S-modules M and N we show that if Tor(p)(s) (M, N) not equal 0, then for 0 less than or equal to i less than or equal to p, the dimension of the K-vector space Tor(i)(s) (M, N) is at least ((p)(i)). In particular, we get lower bounds for the total Betti numbers of such modules. These results are related to a conjecture of Buchsbaum and Eisenbud.
ISSN: 00927872
DOI: 10.1081/AGB-200036803

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