Maximal Betti numbers
Authors:
Marc Chardin, Vesselin Gasharov and Irena Peeva
Journal:
Proc. Amer. Math. Soc. 130 (2002), 18771880
MSC (2000):
Primary 13D02
Published electronically:
February 4, 2002
MathSciNet review:
1896017
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We provide a short proof that the lexicographic ideal has the greatest Betti numbers among all graded ideals with a fixed Hilbert function.
 [Bi]
Anna
Maria Bigatti, Upper bounds for the Betti numbers of a given
Hilbert function, Comm. Algebra 21 (1993),
no. 7, 2317–2334. MR 1218500
(94c:13014), http://dx.doi.org/10.1080/00927879308824679
 [AAH]
Annetta
Aramova, Luchezar
L. Avramov, and Jürgen
Herzog, Resolutions of monomial ideals and
cohomology over exterior algebras, Trans. Amer.
Math. Soc. 352 (2000), no. 2, 579–594. MR 1603874
(2000c:13021), http://dx.doi.org/10.1090/S0002994799022989
 [AHH]
Annetta
Aramova, Jürgen
Herzog, and Takayuki
Hibi, Squarefree lexsegment ideals, Math. Z.
228 (1998), no. 2, 353–378. MR 1630500
(99h:13013), http://dx.doi.org/10.1007/PL00004621
 [EPY]
D. Eisenbud, S. Popescu, and S. Yuzvinsky: Hyperplane arrangements cohomology and monomials in the exterior algebra, Trans. Amer. Math. Soc., to appear.
 [EK]
Shalom
Eliahou and Michel
Kervaire, Minimal resolutions of some monomial ideals, J.
Algebra 129 (1990), no. 1, 1–25. MR 1037391
(91b:13019), http://dx.doi.org/10.1016/00218693(90)90237I
 [Gr]
Mark
L. Green, Generic initial ideals, Six lectures on commutative
algebra (Bellaterra, 1996) Progr. Math., vol. 166, Birkhäuser,
Basel, 1998, pp. 119–186. MR 1648665
(99m:13040)
 [Hu]
Heather
A. Hulett, Maximum Betti numbers of homogeneous ideals with a given
Hilbert function, Comm. Algebra 21 (1993),
no. 7, 2335–2350. MR 1218501
(94c:13015), http://dx.doi.org/10.1080/00927879308824680
 [Bi]
 A. Bigatti: Upper bounds for the Betti numbers of a given Hilbert function, Comm. Algebra 21 (1993), 23172334. MR 94c:13014
 [AAH]
 A. Aramova, L. Avramov, and J. Herzog: Resolutions of monomial ideals and cohomology over exterior algebras, Trans. Amer. Math. Soc. 352 (2000), 579594. MR 2000c:13021
 [AHH]
 A. Aramova, J. Herzog, and T. Hibi: Squarefree lexsegment ideals, Math. Z. 228 (1998), 353378. MR 99h:13013
 [EPY]
 D. Eisenbud, S. Popescu, and S. Yuzvinsky: Hyperplane arrangements cohomology and monomials in the exterior algebra, Trans. Amer. Math. Soc., to appear.
 [EK]
 S. Eliahou and M. Kervaire: Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), 125. MR 91b:13019
 [Gr]
 M. Green: Generic initial ideals, in Six lectures on commutative algebra, Birkhäuser, Progress in Mathematics 166, (1998), 119185. MR 99m:13040
 [Hu]
 H. Hulett: Maximum Betti numbers of homogeneous ideals with a given Hilbert function, Comm. Algebra 21 (1993), 23352350. MR 94c:13015
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Additional Information
Marc Chardin
Affiliation:
Institut de Mathématiques, UMR 7586 du CNRS, Université Pierre et Marie Curie, F75252 Paris Cedex 05, France
Vesselin Gasharov
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14850
Irena Peeva
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14850
Address at time of publication:
Department of Mathematics, Purdue University, West Lafayette, Indiana 479071395
DOI:
http://dx.doi.org/10.1090/S0002993902064717
PII:
S 00029939(02)064717
Received by editor(s):
June 1, 2000
Published electronically:
February 4, 2002
Communicated by:
Michael Stillman
Article copyright:
© Copyright 2002
American Mathematical Society
