Monomials, Binomials, and Riemann-Roch

Details Monomials, Binomials, and Riemann-Roch Monomials, Binomials, and Riemann-Roch

2012-01-20

arxiv.org/abs/1201.4357v1

Mathematics

Commutative Algebra

17 pages, 2 figures

Scientific paper

The Riemann-Roch theorem on a graph G is closely related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration. We also develop a self-contained Riemann-Roch theory for artinian monomial ideals.

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