Algebra & Number Theory

The semigroup of Betti diagrams

Daniel Erman

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The recent proof of the Boij–Söderberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup of such diagrams. We prove that this semigroup is finitely generated, and answer several other fundamental questions about it.

Article information

Algebra Number Theory, Volume 3, Number 3 (2009), 341-365.

Received: 9 November 2008
Revised: 22 January 2009
Accepted: 20 February 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13D25

Boij–Söderberg Theory Betti diagrams Betti tables minimal free resoultions


Erman, Daniel. The semigroup of Betti diagrams. Algebra Number Theory 3 (2009), no. 3, 341--365. doi:10.2140/ant.2009.3.341.

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