Consecutive cancellations in Betti numbers

Author:
Irena Peeva

Journal:
Proc. Amer. Math. Soc. **132** (2004), 3503-3507

MSC (2000):
Primary 13D02

Published electronically:
July 26, 2004

MathSciNet review:
2084070

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Abstract | References | Similar Articles | 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.

**[Ba]**D. Bayer:*The division algorithm and the Hilbert scheme*, Ph.D. Thesis, Harvard University, 1982.**[Ei]**David Eisenbud,*Commutative algebra*, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR**1322960****[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**[ER]**E. Graham Evans Jr. and Benjamin P. Richert,*Possible resolutions for a given Hilbert function*, Comm. Algebra**30**(2002), no. 2, 897–906. MR**1883032**, 10.1081/AGB-120013189**[GHMS]**A. Geramita. T. Harima, J. Migliore, and Y. Shin:*Some remarks on the Hilbert functions of level algebras*, preprint.**[GHS1]**Anthony V. Geramita, Tadahito Harima, and Yong Su Shin,*An alternative to the Hilbert function for the ideal of a finite set of points in ℙⁿ*, Illinois J. Math.**45**(2001), no. 1, 1–23. MR**1849983****[GHS2]**Anthony V. Geramita, Tadahito Harima, and Yong Su Shin,*Decompositions of the Hilbert function of a set of points in ℙⁿ*, Canad. J. Math.**53**(2001), no. 5, 923–943. MR**1859762**, 10.4153/CJM-2001-037-3**[Ha]**Robin Hartshorne,*Connectedness of the Hilbert scheme*, Inst. Hautes Études Sci. Publ. Math.**29**(1966), 5–48. MR**0213368****[Ma]**F. Macaulay:*Some properties of enumeration in the theory of modular systems*, Proc. London Math. Soc.**26**(1927), 531-555.**[Pa]**Keith Pardue,*Deformation classes of graded modules and maximal Betti numbers*, Illinois J. Math.**40**(1996), no. 4, 564–585. MR**1415019****[Ri]**Benjamin P. Richert,*Smallest graded Betti numbers*, J. Algebra**244**(2001), no. 1, 236–259. MR**1856536**, 10.1006/jabr.2001.8878

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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/S0002-9939-04-07517-3

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