Cellular resolutions of Cohen-Macaulay monomial quotient rings

Details Cellular resolutions of Cohen-Macaulay monomial quotient rings Cellular resolutions of Cohen-Macaulay monomial quotient rings

2007-10-17

arxiv.org/abs/0710.3244v2

Journal of commutative algebra, vol. 1, no. 1 (2009), p.57-89

Mathematics

Commutative Algebra

Updated version, 26 pages

Scientific paper

10.1216/JCA-2009-1-1-57

We investigate monomial labellings on cell complexes, giving a minimal cellular resolution of the ideal generated by these monomials, and such that the associated quotient ring is Cohen-Macaulay. We introduce a notion of such a labelling being maximal. There is only a finite number of maximal labellings for each cell complex, and we classify these for trees, partly for subdivisions of polygons, and for some classes of selfdual polytopes.

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