The facet ideal of a simplicial complex |
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Authors: | Sara Faridi |
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Affiliation: | (1) Mathematics Department, George Washington University, Washington, DC 20052. e-mail: faridi@gwu.edu, |
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Abstract: | To a simplicial complex, we associate a square-free monomial ideal in the polynomial ring generated by its vertex set over a field. We study algebraic properties of this ideal via combinatorial properties of the simplicial complex. By generalizing the notion of a tree from graphs to simplicial complexes, we show that ideals associated to trees satisfy sliding depth condition, and therefore have normal and Cohen-Macaulay Rees rings. We also discuss connections with the theory of Stanley-Reisner rings. Received: 7 January 2002 / Revised version: 6 May 2002 |
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