A Riemann-roch Theorem in Tropical Geometry

  title={A Riemann-roch Theorem in Tropical Geometry},
  author={Andreas Gathmann and M. Kerber},
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. Tropical algebraic geometry is a recent branch of mathematics that establishes deep relations between algebro-geometric and purely combinatorial objects. Ideally, every construction and theorem of algebraic geometry should have a tropical (i.e. combinatorial) counterpart that is then… CONTINUE READING



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