Cellular resolutions are a type of combinatorially defined chain complex used by Bayer and Sturmfels to resolve toric ideals. We will use a stratification on the span of a lattice to construct cellular resolutions of a larger class of modules, including the normalizations of quotients of toric ideals. This connects results of Bayer, Popescu, and Sturmfels on resolutions of the diagonal for unimodular toric varieties to recent more general resolutions of the diagonal, as suggested by computational experimentation in Macaulay2.
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