Riemann-Roch theory on finite sets

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

Add a reference to this article to your citeulike library.

Abstract:

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: