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Tropical Linear Series and Tropical Independence
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We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine notion of rank with the notion of tropical independence and has the property that the restriction of a tropical linear series of rank r to a connected subgraph is a tropical linear series of rank r. We show that tropical linear series of rank 1 are finitely generated as tropical modules and state a number of open problems related to algebraic, combinatorial, and topological properties of higher rank tropical linear series
Forward citations
Cited by 3 Pith papers
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Tropical linear series and matroids
Tropical linear series on metric graphs are locally Bergman fans of matroids, yielding an exact condition for canonical tropicalizations to fill the realizable locus.
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Relating Different Definitions of Linear Series on Tropical Curves
A tropical linear series is combinatorial limit if and only if it is structured, and every strongly recursive tropical linear series is combinatorial limit; the reverse inclusion fails from rank three onward.
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Tropical linear systems and the realizability problem
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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