Journal of Commutative Algebra

The cone of Betti tables over three non-collinear points in the plane

Iulia Gheorghita and Steven V Sam

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Abstract

We describe the cone of Betti tables of all finitely generated graded modules over the homogeneous coordinate ring of three non-collinear points in the projective plane. We also describe the cone of Betti tables of all finite length modules.

Article information

Source
J. Commut. Algebra, Volume 8, Number 4 (2016), 537-548.

Dates
First available in Project Euclid: 27 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jca/1477600746

Digital Object Identifier
doi:10.1216/JCA-2016-8-4-537

Mathematical Reviews number (MathSciNet)
MR3566529

Zentralblatt MATH identifier
1367.13010

Subjects
Primary: 13C05: Structure, classification theorems 13D02: Syzygies, resolutions, complexes

Keywords
Boij-Söderberg theory Betti tables free resolutions

Citation

Gheorghita, Iulia; Sam, Steven V. The cone of Betti tables over three non-collinear points in the plane. J. Commut. Algebra 8 (2016), no. 4, 537--548. doi:10.1216/JCA-2016-8-4-537. https://projecteuclid.org/euclid.jca/1477600746


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References

  • Christine Berkesch, Jesse Burke, Daniel Erman and Courtney Gibbons, The cone of Betti diagrams over a hypersurface ring of low embedding dimension, J. Pure Appl. Algebra 216 (2012), 2256–2268.
  • Christine Berkesch, Daniel Erman, Manoj Kummini and Steven V Sam, Shapes of free resolutions over a local ring, Math. Ann. 354 (2012), 939–954.
  • Mats Boij and Jonas Söderberg, Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, J. Lond. Math. Soc. 78 (2008), 85–106.
  • ––––, Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen-Macaulay case, Alg. Num. Th. 6 (2012), 437–454.
  • David Eisenbud and Daniel Erman, Categorified duality in Boij-Söderberg theory and invariants of free complexes, arxiv:1205.0449v2.
  • David Eisenbud and Jürgen Herzog, The classification of homogeneous Cohen-Macaulay rings of finite representation type, Math. Ann. 280 (1988), 347–352.
  • David Eisenbud and Frank-Olaf Schreyer, Betti numbers of graded modules and cohomology of vector bundles, J. Amer. Math. Soc. 22 (2009), 859–888.
  • ––––, Boij-Söderberg theory, in Combinatorial aspects of commutative algebra and algebraic geometry, Abel Symposium 6, Springer, Berlin, 2011, 35–48.
  • Gunnar Fl\oystad, Boij–Söderberg theory: Introduction and survey, in Progress in commutative algebra 1, de Gruyter, Berlin, 2012.
  • Daniel R. Grayson and Michael E. Stillman, Macaulay2, A software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/.
  • J. Herzog and M. Kühl, On the Betti numbers of finite pure and linear resolutions, Comm. Algebra 12 (1984), 1627–1646.
  • Manoj Kummini and Steven V Sam, The cone of Betti tables over a rational normal curve, in Commutative algebra and noncommutative algebraic geometry, Math. Sci. Res. Inst. Publ. 68, Cambridge University Press, Cambridge, 2015, 251–264.
  • Yuji Yoshino, Cohen-Macaulay modules over Cohen-Macaulay rings, Lond. Math. Soc. Lect. Note 146 (1990).