Details:
Title  Monomials, binomials and RiemannRoch.  Author(s)  Madhusudan Manjunath, Bernd Sturmfels  Type  Article in Journal  Abstract  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 Gparking 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 selfcontained 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  ISSN  09259899; 15729192/e 
URL 
http://link.springer.com/article/10.1007%2Fs1080101203869 
Language  English  Journal  J. Algebr. Comb.  Volume  37  Number  4  Pages  737756  Publisher  Springer US, New York, NY  Year  2013  Edition  0  Translation 
No  Refereed 
No 
