Resolutions of facet ideals

Details Resolutions of facet ideals Resolutions of facet ideals

2003-07-17

arxiv.org/abs/math/0307241v1

Mathematics

Commutative Algebra

22 pages

Scientific paper

In this paper we study the resolution of a facet ideal associated with a special class of simplicial complexes introduced by S. Faridi. These simplicial complexes are called trees, and are a generalization (to higher dimensions) of the concept of a tree in graph theory. We show that the Koszul homology of the facet ideal I of a tree is generated by the homology classes of monomial cycles, determine the projective dimension and the regularity of I if the tree is 1-dimensional, show that the graded Betti numbers of I satisfy an alternating sum property if the tree is connected in codimension 1, and classify all trees whose facet ideal has a linear resolution.

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