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On the regularity of -Borel ideals

Author(s): Jürgen Herzog; Dorin Popescu
Journal: Proc. Amer. Math. Soc. 129 (2001), 2563-2570.
MSC (1991): Primary 13P10; Secondary 13D02, 13C13
Posted: February 9, 2001
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Abstract:

In this paper we prove Pardue's conjecture on the regularity of principal -Borel ideals. As a consequence we obtain an upper bound for the regularity of general -Borel ideals.

References:

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2.: D. Bayer and M. Stillman, A criterion for detecting -regularity, Invent. Math. 87 (1987), 1-11. MR 87k:13019
3.: S. Eliahou and M. Kervaire, Minimal resolutions of some monomial ideals, J. of Algebra 129 (1990) 1-25. MR 91b:13019
4.: D. Eisenbud, A. Reeves and B. Totaro, Initial ideals, Veronese subrings, and rates of algebras, Adv Math. 109 (1994), 168-187. MR 96d:13030
5.: V. Ene, G. Pfister and D. Popescu, Betti numbers for -stable ideals, Comm. Algebra 28 (2000), 1515-1531. CMP 2000:08
6.: K. Pardue, Nonstandard Borel-fixed ideals, Dissertation, Brandeis University, 1994.


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