Consecutive cancellations in Betti numbers
Author:
Irena Peeva
Journal:
Proc. Amer. Math. Soc. 132 (2004), 35033507
MSC (2000):
Primary 13D02
Published electronically:
July 26, 2004
MathSciNet review:
2084070
Fulltext PDF Free Access
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References 
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Additional Information
Abstract: Let be a homogeneous ideal in a polynomial ring over a field. By Macaulay's Theorem, there exists a lexicographic ideal with the same Hilbert function as . We prove that the graded Betti numbers of are obtained from those of by a sequence of consecutive cancellations.
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 [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, SpringerVerlag, New York, 1995. MR 97a:13001
 [EK]
 S. Eliahou and M. Kervaire: Minimal resolutions of some monomial ideals, J. Algebra, 129 (1990), 125. MR 91b:13019
 [ER]
 G. Evans and B. Richert: Possible resolutions for a given Hilbert function, Communications in Algebra 30 (2002), 897906. 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 , Illinois J. Math. 45 (2001), 123. MR 2002g:13004
 [GHS2]
 A. Geramita. T. Harima, and Y. Shin: Decompositions of the Hilbert function of a set of points in , Canad. J. Math. 53 (2001), 923943. MR 2002i:13019
 [Ha]
 R. Hartshorne: Connectedness of the Hilbert scheme, Publications Mathématiques IHES 29 (1966), 548. MR 35:4232
 [Ma]
 F. Macaulay: Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. 26 (1927), 531555.
 [Pa]
 K. Pardue: Deformation classes of graded modules and maximal Betti numbers, Illinois J. Math. 40 (1996), 564585. MR 97g:13029
 [Ri]
 B. Richert: Smallest graded Betti numbers, J. Algebra 244 (2001), 236259.MR 2002g:13024
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Additional Information
Irena Peeva
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853
DOI:
http://dx.doi.org/10.1090/S0002993904075173
PII:
S 00029939(04)075173
Keywords:
Syzygies
Received by editor(s):
November 21, 2002
Received by editor(s) in revised form:
August 25, 2003
Published electronically:
July 26, 2004
Communicated by:
Michael Stillman
Article copyright:
© Copyright 2004
American Mathematical Society
