Monomials, Binomials, and Riemann-Roch

Madhusudan Manjunath; Bernd Sturmfels

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arXiv · 1201.4357

Monomials, Binomials, and Riemann-Roch

Madhusudan Manjunath·Bernd Sturmfels

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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.

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BibTeX RIS

Madhusudan Manjunath, Bernd Sturmfels. 2012-07-09. Monomials, Binomials, and Riemann-Roch. https://arxiv.org/abs/1201.4357

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