A Riemann–Roch theorem in tropical geometry
First Online: 19 July 2007 Received: 22 December 2006 Accepted: 06 June 2007 DOI:
Cite this article as: Gathmann, A. & Kerber, M. Math. Z. (2008) 259: 217. doi:10.1007/s00209-007-0222-4 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.
Mathematics Subject Classification (2000) Primary 14N35 51M20 Secondary 14N10 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.
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