Mathematical Research Letters

Volume 17 (2010)

Number 5

The linear space of Betti diagrams of multigraded artinian modules

Pages: 943 – 958



Gunnar Floystad (Matematisk Institutt, University of Bergen, Johs. Brunsgt. 12, 5008 Bergen, Norway)


We study the linear space generated by the multigraded Betti diagrams of $\hele^n$-graded artinian modules of codimension $n$ whose resolutions become pure of a given type when taking total degrees. We show that the multigraded Betti diagram of the equivariant resolution constructed in \cite{EFW} by D.Eisenbud, J.Weyman, and the author, and all its twists, form a basis for this linear space. We also show that it is essentially unique with this property.

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