In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The problem is finiteness. The i local cohomol...

Baker-Beynon duality theory yields a concrete representation of any finitely generated projective Abelian lattice-ordered group G in terms of piecewise linear homogeneous functions with integer coefficients, defined over the support |Σ| of a fan Σ. A unimodular fan ∆ over |Σ| determines a Schauder basis ofG: its elements are the minimal positive free generators of the pointwise ordered group of...