### Abstract

In [J. Herzog, H. Srinivasan, Bounds for multiplicities, Trans. Amer. Math. Soc. 350 (1998) 2879-2902], Herzog and Srinivasan study the relationship between the graded Betti numbers of a homogeneous ideal I in a polynomial ring R and the degree of I. For certain classes of ideals, they prove a bound on the degree in terms of the largest and smallest Betti numbers, generalizing results of Huneke and Miller in [C. Huneke, M. Miller, A note on the multiplicity of Cohen-Macaulay algebras with pure resolutions, Canad. J. Math. 37 (1985) 1149-1162]. The bound is conjectured to hold in general; we study this using linkage. If R / I is Cohen-Macaulay, we may reduce to the case where I defines a zero-dimensional subscheme Y. If Y is residual to a zero-scheme Z of a certain type (low degree or points in special position), then we show that the conjecture is true for I_{Y}.

Original language | English (US) |
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Pages (from-to) | 481-491 |

Number of pages | 11 |

Journal | Journal of Pure and Applied Algebra |

Volume | 210 |

Issue number | 2 |

DOIs | |

State | Published - Aug 2007 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Journal of Pure and Applied Algebra*,

*210*(2), 481-491. https://doi.org/10.1016/j.jpaa.2006.10.017