A Riemann–Roch theorem in tropical geometry
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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- 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
- 2.Gathmann, A., Markwig, H.: Kontsevich’s formula and the WDVV equations in tropical geometry. Preprint math.AG/0509628Google Scholar
- 3.Mikhalkin, G., Zharkov, I.: Tropical curves, their Jacobians and Theta functions. preprint math. AG/0612267Google Scholar