Abstract
Recently, Baker and Norine have proven a Riemann–Roch theorem for finite graphs. We extend their results to metric graphs and thus establish a Riemann–Roch theorem for divisors on (abstract) tropical curves.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Baker, M., Norine, S.: Riemann–Roch and Abel–Jacobi theory on a finite graph. Adv. Math. (to appear, 2007), preprint math.CO/0608360
Gathmann, A., Markwig, H.: Kontsevich’s formula and the WDVV equations in tropical geometry. Preprint math.AG/0509628
Mikhalkin, G., Zharkov, I.: Tropical curves, their Jacobians and Theta functions. preprint math. AG/0612267
Zhang S. (1993). Admissible pairing on a curve. Invent. Math. 112: 171–193
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gathmann, A., Kerber, M. A Riemann–Roch theorem in tropical geometry. Math. Z. 259, 217–230 (2008). https://doi.org/10.1007/s00209-007-0222-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00209-007-0222-4