Cellular Resolutions Of Cohen-Macaulay Monomial Ideals

Abstract

We investigate monomial labelings 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 labeling being maximal. There is only a finitenumber of maximal such labelings for each cell complex, and we classify these for trees, subdivisions of polygons, and some classes of selfdual polytopes. © 2009 Rocky Mountain Mathematics Consortium.