Cellular resolutions of cointerval ideals

Details Cellular resolutions of cointerval ideals Cellular resolutions of cointerval ideals

2010-04-05

arxiv.org/abs/1004.0713v2

Mathematics

Commutative Algebra

23 pages, 11 figures. Minor revisions and corrections, title slightly modified.

Scientific paper

Minimal cellular resolutions of the edge ideals of cointerval hypergraphs are constructed. This class of d-uniform hypergraphs coincides with the complements of interval graphs (for the case d=2), and strictly contains the class of `strongly stable' hypergraphs corresponding to pure shifted simplicial complexes. The polyhedral complexes supporting the resolutions are described as certain spaces of directed graph homomorphisms, and are realized as subcomplexes of mixed subdivisions of the Minkowski sums of simplices. Resolutions of more general hypergraphs are obtained by considering decompositions into cointerval hypergraphs.

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