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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some Ideals with Large Projective Dimension


Authors: Giulio Caviglia and Manoj Kummini
Journal: Proc. Amer. Math. Soc. 136 (2008), 505-509
MSC (2000): Primary 13D05; Secondary 13C15
Published electronically: October 25, 2007
MathSciNet review: 2358490
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Abstract | References | Similar Articles | Additional Information

Abstract: For an ideal $ I$ in a polynomial ring over a field, a monomial support of $ I$ is the set of monomials that appear as terms in a set of minimal generators of $ I$. Craig Huneke asked whether the size of a monomial support is a bound for the projective dimension of the ideal. We construct an example to show that, if the number of variables and the degrees of the generators are unspecified, the projective dimension of $ I$ grows at least exponentially with the size of a monomial support. The ideal we construct is generated by monomials and binomials.


References [Enhancements On Off] (What's this?)

  • [Eis95] David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960 (97a:13001)
  • [Eis05] David Eisenbud, The geometry of syzygies, Graduate Texts in Mathematics, vol. 229, Springer-Verlag, New York, 2005. A second course in commutative algebra and algebraic geometry. MR 2103875 (2005h:13021)
  • [Eng05] Bahman Engheta, Bounds on projective dimension, Ph.D. thesis, University of Kansas, Lawrence, KS, 2005.

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Additional Information

Giulio Caviglia
Affiliation: Department of Mathematics, University of California, Berkeley, California
Email: caviglia@math.berkeley.edu

Manoj Kummini
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas
Email: kummini@math.ku.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09159-9
PII: S 0002-9939(07)09159-9
Keywords: Projective resolutions, monomial support
Received by editor(s): October 16, 2006
Received by editor(s) in revised form: February 11, 2007
Published electronically: October 25, 2007
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.