Geodesic
The Brill-Noether rank of a tropical curve
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 841-860.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 algebraic curve.
Classification : 14T05
Keywords: tropical curves, divisors, linear systems 
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     author = {Len, Yoav},
     title = {The {Brill-Noether} rank of a tropical curve},
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Len, Yoav. The Brill-Noether rank of a tropical curve. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 841-860. http://geodesic.mathdoc.fr/item/JAC_2014__40_3_a1/