Mathematische Zeitschrift

, Volume 259, Issue 1, pp 217–230 | Cite as

A Riemann–Roch theorem in tropical geometry

Article

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 

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References

  1. 1.
    Baker, M., Norine, S.: Riemann–Roch and Abel–Jacobi theory on a finite graph. Adv. Math. (to appear, 2007), preprint math.CO/0608360Google Scholar
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    Gathmann, A., Markwig, H.: Kontsevich’s formula and the WDVV equations in tropical geometry. Preprint math.AG/0509628Google Scholar
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    Mikhalkin, G., Zharkov, I.: Tropical curves, their Jacobians and Theta functions. preprint math. AG/0612267Google Scholar
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    Zhang S. (1993). Admissible pairing on a curve. Invent. Math. 112: 171–193 MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Fachbereich MathematikTU KaiserslauternKaiserslauternGermany

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