Geodesic
Monomials, binomials and Riemann-Roch
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 4, pp. 737-756.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The Riemann-Roch theorem on a graph G is related to Alexander duality in combinatorial commutative 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.
Keywords: Riemann-Roch theory for graphs, combinatorial commutative algebra, chip firing games, Laplacian matrix of a graph, lattice ideals and their Betti numbers, Alexander duality of monomial ideals, scarf complex 
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     author = {Manjunath, Madhusudan and Sturmfels, Bernd},
     title = {Monomials, binomials and {Riemann-Roch}},
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Manjunath, Madhusudan; Sturmfels, Bernd. Monomials, binomials and Riemann-Roch. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 4, pp. 737-756. http://geodesic.mathdoc.fr/item/JAC_2013__37_4_a2/