Algebra & Number Theory · 2008 · 215 citations · 13 references
Natural SciencesMathematicsComputational GeometryGeometryNumber TheoryAlgebraic GeometryArithmetic GeometryDifferential GeometryArithmetic TheoryDiscrete Valuation RingsRational CurvesRational Points On Varieties
Abstract. We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and tropical geometry. 1.
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Tropical Geometry and its applications
Grigory Mikhalkin · ArXiv.org · 2006 · 241 citations · Full text
A Riemann–Roch theorem in tropical geometry
Andreas Gathmann, Michael Kerber · Mathematische Zeitschrift · 2007 · 174 citations