Abstract
We describe the positive cone generated by bigraded Betti diagrams of artinian modules of codimension two, whose resolutions become pure of a given type when taking total degrees. If the differences, p and q, of these total degrees are relatively prime, the extremal rays are parametrized by order ideals in ℕ2 contained in the region px+qy<(p−1)(q−1). We also consider some examples concerning artinian modules of codimension three.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Boij, J. Söderberg, Graded Betti numbers of Cohen–Macaulay modules and the multiplicity conjecture, Journal of the London Mathematical Society, 78, no. 1 (2008), p. 78–101.
D. Eisenbud, G. Fløystad, J. Weyman, The existence of pure free resolutions, arXiv:0709.1529, to appear in Annales de l’institut Fourier.
D. Eisenbud, F.-O. Schreyer, Betti numbers of graded modules and cohomology of vector bundles, Journal of the American Mathematical Society 22 (2009), p. 859–888.
G. Fløystad, The linear space of Betti diagrams of multigraded artinian modules, Mathematical Research Letters, 17, no. 5 (2010), p. 943–958.
W. Fulton, J. Harris, Representation theory, GTM 129, Springer Verlag 1991.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boij, M., Fløystad, G. (2011). The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two. In: Fløystad, G., Johnsen, T., Knutsen, A. (eds) Combinatorial Aspects of Commutative Algebra and Algebraic Geometry. Abel Symposia, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19492-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-19492-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19491-7
Online ISBN: 978-3-642-19492-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)