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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 $I$ 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.

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Additional Information

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

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