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arXiv · 1209.6309

The Brill-Noether rank of a tropical curve

Yoav Len
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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.

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Yoav Len. 2012-09-27. The Brill-Noether rank of a tropical curve. https://doi.org/10.1007/s10801-014-0510-0

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