Geodesic
Tropical hyperelliptic curves
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 2, pp. 331-359.

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

Summary: We study the locus of tropical hyperelliptic curves inside the moduli space of tropical curves of genus g. We define a harmonic morphism of metric graphs and prove that a metric graph is hyperelliptic if and only if it admits a harmonic morphism of degree 2 to a metric tree. This generalizes the work of Baker and Norine on combinatorial graphs to the metric case. We then prove that the locus of 2-edge-connected genus g tropical hyperelliptic curves is a (2g - 1)-dimensional stacky polyhedral fan whose maximal cells are in bijection with trees on g - 1 vertices with maximum valence 3. Finally, we show that the Berkovich skeleton of a classical hyperelliptic plane curve satisfying a certain tropical smoothness condition is a standard ladder of genus g.
Keywords: tropical geometry, tropical curves, hyperelliptic curves, metric graphs, harmonic morphisms 
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     author = {Chan, Melody},
     title = {Tropical hyperelliptic curves},
     journal = {Journal of Algebraic Combinatorics},
     pages = {331--359},
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     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__37_2_a2/}
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Chan, Melody. Tropical hyperelliptic curves. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 2, pp. 331-359. http://geodesic.mathdoc.fr/item/JAC_2013__37_2_a2/