Monomials, Binomials, and Riemann-Roch
Commutative Algebra
2012-07-11 v2 Discrete Mathematics
Combinatorics
Abstract
The Riemann-Roch theorem on a graph G is 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.
Cite
@article{arxiv.1201.4357,
title = {Monomials, Binomials, and Riemann-Roch},
author = {Madhusudan Manjunath and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1201.4357},
year = {2012}
}
Comments
18 pages, 2 figures, Minor revisions