Maximal Betti numbers

Authors:
Marc Chardin, Vesselin Gasharov and Irena Peeva

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1877-1880

MSC (2000):
Primary 13D02

Published electronically:
February 4, 2002

MathSciNet review:
1896017

Full-text PDF Free Access

Abstract | References | Similar Articles | 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**, 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**, 10.1090/S0002-9947-99-02298-9**[AHH]**Annetta Aramova, Jürgen Herzog, and Takayuki Hibi,*Squarefree lexsegment ideals*, Math. Z.**228**(1998), no. 2, 353–378. MR**1630500**, 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**, 10.1016/0021-8693(90)90237-I**[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****[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**, 10.1080/00927879308824680

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
13D02

Retrieve articles in all journals with MSC (2000): 13D02

Additional Information

**Marc Chardin**

Affiliation:
Institut de Mathématiques, UMR 7586 du CNRS, Université Pierre et Marie Curie, F-75252 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 47907-1395

DOI:
https://doi.org/10.1090/S0002-9939-02-06471-7

Received by editor(s):
June 1, 2000

Published electronically:
February 4, 2002

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2002
American Mathematical Society