Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Consecutive cancellations in Betti numbers

Author(s): Irena Peeva
Journal: Proc. Amer. Math. Soc. 132 (2004), 3503-3507.
MSC (2000): Primary 13D02
Posted: July 26, 2004
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Let $I$ be a homogeneous ideal in a polynomial ring over a field. By Macaulay's Theorem, there exists a lexicographic ideal $L$ with the same Hilbert function as $I$. We prove that the graded Betti numbers of $I$ are obtained from those of $L$ by a sequence of consecutive cancellations.

References:

[Ba]
D. Bayer: The division algorithm and the Hilbert scheme, Ph.D. Thesis, Harvard University, 1982.

[Ei]
D. Eisenbud: Commutative Algebra with a View Towards Algebraic Geometry, Springer-Verlag, New York, 1995. MR 97a:13001

[EK]
S. Eliahou and M. Kervaire: Minimal resolutions of some monomial ideals, J. Algebra, 129 (1990), 1-25. MR 91b:13019

[ER]
G. Evans and B. Richert: Possible resolutions for a given Hilbert function, Communications in Algebra 30 (2002), 897-906. MR 2002k:13024

[GHMS]
A. Geramita. T. Harima, J. Migliore, and Y. Shin: Some remarks on the Hilbert functions of level algebras, preprint.

[GHS1]
A. Geramita. T. Harima, and Y. Shin: An alternative to the Hilbert function for the ideal of a finite set of points in $\mathbf{P}^n$, Illinois J. Math. 45 (2001), 1-23. MR 2002g:13004

[GHS2]
A. Geramita. T. Harima, and Y. Shin: Decompositions of the Hilbert function of a set of points in $\mathbf{P}^n$, Canad. J. Math. 53 (2001), 923-943. MR 2002i:13019

[Ha]
R. Hartshorne: Connectedness of the Hilbert scheme, Publications Mathématiques IHES 29 (1966), 5-48. MR 35:4232

[Ma]
F. Macaulay: Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. 26 (1927), 531-555.

[Pa]
K. Pardue: Deformation classes of graded modules and maximal Betti numbers, Illinois J. Math. 40 (1996), 564-585. MR 97g:13029

[Ri]
B. Richert: Smallest graded Betti numbers, J. Algebra 244 (2001), 236-259.MR 2002g:13024

Similar Articles:

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

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

Additional Information:

Irena Peeva
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853

DOI: 10.1090/S0002-9939-04-07517-3
PII: S 0002-9939(04)07517-3
Keywords: Syzygies
Received by editor(s): November 21, 2002
Received by editor(s) in revised form: August 25, 2003
Posted: July 26, 2004
Communicated by: Michael Stillman
Copyright of article: Copyright 2004, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google