The Brill-Noether rank of a tropical curve

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11 Citations (Scopus)

Abstract

We construct a space classifying divisor classes of a fixed degree on all tropical curves of a fixed combinatorial type and show that the function taking a divisor class to its rank is upper semicontinuous. We extend the definition of the Brill-Noether rank of a metric graph to tropical curves and use the upper semicontinuity of the rank function on divisors to show that the Brill-Noether rank varies upper semicontinuously in families of tropical curves. Furthermore, we present a specialization lemma relating the Brill-Noether rank of a tropical curve with the dimension of the Brill-Noether locus of an algerbaic curve.
Original languageEnglish
Pages (from-to)841-860
Number of pages20
JournalJournal of Algebraic Combinatorics
Volume40
Issue number3
DOIs
Publication statusPublished - 2014

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