Minimal monomial ideals and linear resolutions

Jeffry Phan

Minimal monomial ideals and linear resolutions

交换代数 2007-05-23 v2 组合数学

作者: Jeffry Phan

摘要

A minimal monomial ideal is the combinatorially simplest monomial ideal whose lcm-lattice equals a given finite atomic lattice $\hat{L}$ . The minimal ideal inherits many nice properties of any ideal $I$ whose lcm-lattice also equals $\hat{L}$ , e.g. Cohen-Macaulayness and the dual property of having a linear resolution. Conversely, any ideal having a linear resolution is shown to be (essentially) minimal.

关键词

monomial ideals and free resolutions ideal theory monomial ideals

引用

@article{arxiv.math/0511032,
  title  = {Minimal monomial ideals and linear resolutions},
  author = {Jeffry Phan},
  journal= {arXiv preprint arXiv:math/0511032},
  year   = {2007}
}

备注

14 pages, 4 figures. 2 corrections have been made: (1) The hypothesis in Proposition 2.6 have been corrected to exclude the boundary complex of a simplex. (2) The labeling of the triangle in Figure 2 has been corrected

Minimal monomial ideals and linear resolutions

摘要

关键词

引用

备注

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