Schottky Algorithms: Classical meets Tropical

Lynn Chua, Mario Denis Kummer, and Bernd Sturmfels

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Submission date: 27. Jul. 2017
published in: Mathematics of computation, 88 (2019) 319, p. 2541-2558 
DOI number (of the published article): 10.1090/mcom/3406
Bibtex
Link to arXiv: See the arXiv entry of this preprint.

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.