Riemann-Roch and Abel-Jacobi theory on a finite graph
| dc.creator | Baker, Matthew | |
| dc.creator | Norine, Serguei | |
| dc.date | 2006-08-14 | |
| dc.date | 2007-07-09 | |
| dc.date.accessioned | 2026-07-07T08:14:25Z | |
| dc.date.available | 2026-07-07T08:14:25Z | |
| dc.description | It is well-known that a finite graph can be viewed, in many respects, as a discrete analogue of a Riemann surface. In this paper, we pursue this analogy further in the context of linear equivalence of divisors. In particular, we formulate and prove a graph-theoretic analogue of the classical Riemann-Roch theorem. We also prove several results, analogous to classical facts about Riemann surfaces, concerning the Abel-Jacobi map from a graph to its Jacobian. As an application of our results, we characterize the existence or non-existence of a winning strategy for a certain chip-firing game played on the vertices of a graph. | |
| dc.description | 35 pages. v3: Several minor changes made, mostly fixing typographical errors. This is the final version, to appear in Adv. Math | |
| dc.identifier | https://arxiv.org/abs/math/0608360 | |
| dc.identifier | http://arxiv.org/abs/math/0608360 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133118 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | Riemann-Roch and Abel-Jacobi theory on a finite graph | |
| dc.type | text |