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Specialization of linear systems from curves to graphs

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arxiv math/0701075 v4 pith:LHUBAFHP submitted 2007-01-02 math.NT math.AGmath.CO

Matthew Baker This is my paper · ORCID
classification math.NTmath.AGmath.CO
keywords arithmeticcurvesgeometrygraphslinearspecializationsystemsapplications
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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.

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  1. Tropical linear systems and the realizability problem

    math.AG 2025-06 conditional novelty 6.0 of 10

    Local dimension of a tropical linear system is bounded below by its Baker-Norine rank, and the realizable canonical divisors form a tropically convex, definable, closed polyhedral complex.

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