Riemann-Roch theory on finite sets

Rodney James and Rick Miranda

Journal of Singularities
volume 9 (2014), 75-81

Received 29 January 2012. Received in revised form 2 July 2014.

DOI: 10.5427/jsing.2014.9g

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M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In earlier works, we generalized these concepts to real-valued functions, and proved a corresponding Riemann-Roch Theorem in that setting, showing that it implied the Baker-Norine result. In this article we prove a Riemann-Roch Theorem in a more general combinatorial setting that is not necessarily driven by the existence of a graph.

Author(s) information:

Rodney James Rick Miranda
Dept. of Mathematics and Computer Science Dept. of Mathematics
Colorado College Colorado State University
Colorado Springs, CO, USA Fort Collins, CO, USA