## Some Ideals with Large Projective Dimension

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- by Giulio Caviglia and Manoj Kummini PDF
- Proc. Amer. Math. Soc.
**136**(2008), 505-509 Request permission

## 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

- David Eisenbud,
*Commutative algebra*, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR**1322960**, DOI 10.1007/978-1-4612-5350-1 - 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** - Bahman Engheta,
*Bounds on projective dimension*, Ph.D. thesis, University of Kansas, Lawrence, KS, 2005.

## 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
- MR Author ID: 827227
- ORCID: 0000-0002-4822-0112
- Email: kummini@math.ku.edu
- 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
- © Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**136**(2008), 505-509 - MSC (2000): Primary 13D05; Secondary 13C15
- DOI: https://doi.org/10.1090/S0002-9939-07-09159-9
- MathSciNet review: 2358490