Cellular resolutions of Cohen-Macaulay monomial quotient rings
arXiv:0710.3244 · doi:10.1216/JCA-2009-1-1-57
Abstract
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.
Updated version, 26 pages