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The possible extremal Betti numbers of a homogeneous ideal

Authors: Jürgen Herzog, Leila Sharifan and Matteo Varbaro
Journal: Proc. Amer. Math. Soc. 142 (2014), 1875-1891
MSC (2010): Primary 13D02
Published electronically: February 27, 2014
MathSciNet review: 3182008
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Abstract: We give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of any homogeneous ideal in a polynomial ring over a field of characteristic 0.

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  • [AHH] Annetta Aramova, Jürgen Herzog, and Takayuki Hibi, Ideals with stable Betti numbers, Adv. Math. 152 (2000), no. 1, 72-77. MR 1762120 (2001d:13012),
  • [BCP] Dave Bayer, Hara Charalambous, and Sorin Popescu, Extremal Betti numbers and applications to monomial ideals, J. Algebra 221 (1999), no. 2, 497-512. MR 1726711 (2001a:13020),
  • [BH] Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956 (95h:13020)
  • [Co] CoCoA Team, CoCoA: a system for doing Computations in Commutative Algebra, available at
  • [CHH] Aldo Conca, Jürgen Herzog, and Takayuki Hibi, Rigid resolutions and big Betti numbers, Comment. Math. Helv. 79 (2004), no. 4, 826-839. MR 2099124 (2005k:13025),
  • [ER] John A. Eagon and Victor Reiner, Resolutions of Stanley-Reisner rings and Alexander duality, J. Pure Appl. Algebra 130 (1998), no. 3, 265-275. MR 1633767 (99h:13017),
  • [Ei] David Eisenbud, Commutative algebra.: With a view toward algebraic geometry., Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. MR 1322960 (97a:13001)
  • [EK] Shalom Eliahou and Michel Kervaire, Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), no. 1, 1-25. MR 1037391 (91b:13019),
  • [HH1] Jürgen Herzog and Takayuki Hibi, Componentwise linear ideals, Nagoya Math. J. 153 (1999), 141-153. MR 1684555 (2000i:13019)
  • [HH2] Jürgen Herzog and Takayuki Hibi, Monomial ideals, Graduate Texts in Mathematics, vol. 260, Springer-Verlag London Ltd., London, 2011. MR 2724673 (2011k:13019)
  • [Mu] Satoshi Murai, Hilbert functions of $ d$-regular ideals, J. Algebra 317 (2007), no. 2, 658-690. MR 2362936 (2008i:13027),
  • [NR] U. Nagel and T. Römer, Criteria for componentwise linearity, available at arXiv:1108.3921v2, 2011.

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Additional Information

Jürgen Herzog
Affiliation: Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany

Leila Sharifan
Affiliation: Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran

Matteo Varbaro
Affiliation: Dipartimento di Matematica, Università degli Studi di Genova, Genova, Italy

Keywords: Betti tables, componentwise linear ideals, extremal Betti numbers, strongly stable monomial ideals
Received by editor(s): December 24, 2011
Received by editor(s) in revised form: May 26, 2012, and July 2, 2012
Published electronically: February 27, 2014
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society

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