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arXiv · 1707.08520

Schottky Algorithms: Classical meets Tropical

Lynn Chua·Mario Kummer·Bernd Sturmfels
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Abstract

We present a new perspective on the Schottky problem that links numerical computing with tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and, if so, to compute the curve and its canonical embedding. We offer solutions and their implementations in genus four, both classically and tropically. The locus of cographic matroids arises from tropicalizing the Schottky-Igusa modular form.

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Lynn Chua, Mario Kummer, Bernd Sturmfels. 2018-09-30. Schottky Algorithms: Classical meets Tropical. https://doi.org/10.1090/mcom%2F3406

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