Tropical curves of hyperelliptic type

Algebra Seminar
Tuesday, November 5, 2019 - 1:30pm for 1 hour (actually 50 minutes)
Skiles 005
Daniel Corey – University of Wisconsin – dcorey@math.wisc.edu
Yoav Len

We introduce the notion of tropical curves of hyperelliptic type. These are tropical curves whose Jacobian is isomorphic to that of a hyperelliptic tropical curve, as polarized tropical abelian varieties. Using the tropical Torelli theorem (due to Caporaso and Viviani), this characterization may be phrased in terms of 3-edge connectiviations. We show that being of hyperelliptic type is independent of the edge lengths and is preserved when passing to genus ≥2 connected minors. The main result is an excluded minors characterization of tropical curves of hyperelliptic type.