Minimal monomial ideals and linear resolutions
Abstract
Description
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.
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
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